Download Graduate Aptitude Test in Engineering (GATE) 2015 XE D Engineering Sciences Question Paper
XE-D 1/8
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 Find the force (in kN) in the member BH of the truss shown.
Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having side length a.
At point B, the equivalent force and couple are, respectively,
(A) F( ?) and 3 ?3Fa (clockwise)
(B) F( ?) and ?3Fa (clockwise)
(C) F( ?) and ?3Fa (counter clockwise)
(D) F( ?) and 3 ?3Fa (counter clockwise)
Q.3 Bar-1 has a diameter d, length L, and elastic modulus E and subjected to tensile load P, resulting in
an elongation of ?
1
. Bar-2 has diameter, 2d, length 2L, an elastic modulus 2E and subjected to
tensile load 2P, resulting in an elongation of ?
2
. Find the ratio ?
1
/ ?
2
.
Q.4 In a plane stress problem, the principal stresses at a point are 30MPa and -15MPa. At the same
point, on an element whose sides make an angle of 45
o
with respect to the principal axes, the
normal stresses (in MPa) are
(A) 15/2 and 15/2 (B) 30/2 and 30/2 (C) 15/2 and -15/2 (D) 30/2 and -30/2
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GATE 2015 SOLID MECHANICS ? XE-D
XE-D 1/8
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 Find the force (in kN) in the member BH of the truss shown.
Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having side length a.
At point B, the equivalent force and couple are, respectively,
(A) F( ?) and 3 ?3Fa (clockwise)
(B) F( ?) and ?3Fa (clockwise)
(C) F( ?) and ?3Fa (counter clockwise)
(D) F( ?) and 3 ?3Fa (counter clockwise)
Q.3 Bar-1 has a diameter d, length L, and elastic modulus E and subjected to tensile load P, resulting in
an elongation of ?
1
. Bar-2 has diameter, 2d, length 2L, an elastic modulus 2E and subjected to
tensile load 2P, resulting in an elongation of ?
2
. Find the ratio ?
1
/ ?
2
.
Q.4 In a plane stress problem, the principal stresses at a point are 30MPa and -15MPa. At the same
point, on an element whose sides make an angle of 45
o
with respect to the principal axes, the
normal stresses (in MPa) are
(A) 15/2 and 15/2 (B) 30/2 and 30/2 (C) 15/2 and -15/2 (D) 30/2 and -30/2
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 2/8
Q.5 Two systems shown below start from rest. For the system shown on the left, two 50N blocks are
connected by a cord. For the system shown on the right, the 50N block is pulled by a 50N
downward force. Neglect friction. Which of the following is true?
(A) Blocks A and C have the same acceleration.
(B) Block C will have a larger acceleration than block A.
(C) Block A will have a larger acceleration than block C.
(D) Block A will not move.
Q.6 Two massless rigid bars, each of length a = 0.5m, are connected by a rotational spring having
stiffness k = 1000 N.m/rad. Find the buckling load P (in kN).
Q.7 A simply supported beam having a rectangular cross-section of depth d is subjected to a vertical
concentrated load P at the mid-span. The maximum shear stress in a section occurs at
(A) d/2 from the top of the cross-section
(B) d/3 from the top of the cross-section
(C) 2d/3 from the top of the cross-section
(D) Top of the cross-section
Q.8 A steel block of size 100?50?25 mm
3
is subjected to a uniform pressure on all faces. The
dimension of the 100mm edge reduces by 25?m (note 1 ?m = 10
-6
m). Find the applied pressure (in
GPa). Use E = 240 GPa and ? = 0.3.
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GATE 2015 SOLID MECHANICS ? XE-D
XE-D 1/8
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 Find the force (in kN) in the member BH of the truss shown.
Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having side length a.
At point B, the equivalent force and couple are, respectively,
(A) F( ?) and 3 ?3Fa (clockwise)
(B) F( ?) and ?3Fa (clockwise)
(C) F( ?) and ?3Fa (counter clockwise)
(D) F( ?) and 3 ?3Fa (counter clockwise)
Q.3 Bar-1 has a diameter d, length L, and elastic modulus E and subjected to tensile load P, resulting in
an elongation of ?
1
. Bar-2 has diameter, 2d, length 2L, an elastic modulus 2E and subjected to
tensile load 2P, resulting in an elongation of ?
2
. Find the ratio ?
1
/ ?
2
.
Q.4 In a plane stress problem, the principal stresses at a point are 30MPa and -15MPa. At the same
point, on an element whose sides make an angle of 45
o
with respect to the principal axes, the
normal stresses (in MPa) are
(A) 15/2 and 15/2 (B) 30/2 and 30/2 (C) 15/2 and -15/2 (D) 30/2 and -30/2
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 2/8
Q.5 Two systems shown below start from rest. For the system shown on the left, two 50N blocks are
connected by a cord. For the system shown on the right, the 50N block is pulled by a 50N
downward force. Neglect friction. Which of the following is true?
(A) Blocks A and C have the same acceleration.
(B) Block C will have a larger acceleration than block A.
(C) Block A will have a larger acceleration than block C.
(D) Block A will not move.
Q.6 Two massless rigid bars, each of length a = 0.5m, are connected by a rotational spring having
stiffness k = 1000 N.m/rad. Find the buckling load P (in kN).
Q.7 A simply supported beam having a rectangular cross-section of depth d is subjected to a vertical
concentrated load P at the mid-span. The maximum shear stress in a section occurs at
(A) d/2 from the top of the cross-section
(B) d/3 from the top of the cross-section
(C) 2d/3 from the top of the cross-section
(D) Top of the cross-section
Q.8 A steel block of size 100?50?25 mm
3
is subjected to a uniform pressure on all faces. The
dimension of the 100mm edge reduces by 25?m (note 1 ?m = 10
-6
m). Find the applied pressure (in
GPa). Use E = 240 GPa and ? = 0.3.
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 3/8
Q.9 Which one of the following statements is true?
(A) In a tensile test on a rod made of ductile material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(B) In a tensile test on a rod made of brittle material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(C) In a torsion test on a rod made of ductile material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(D) In a torsion test on a rod made of brittle material, failure occurs along a plane making 0
o
with
respect to the axis of the rod
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GATE 2015 SOLID MECHANICS ? XE-D
XE-D 1/8
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 Find the force (in kN) in the member BH of the truss shown.
Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having side length a.
At point B, the equivalent force and couple are, respectively,
(A) F( ?) and 3 ?3Fa (clockwise)
(B) F( ?) and ?3Fa (clockwise)
(C) F( ?) and ?3Fa (counter clockwise)
(D) F( ?) and 3 ?3Fa (counter clockwise)
Q.3 Bar-1 has a diameter d, length L, and elastic modulus E and subjected to tensile load P, resulting in
an elongation of ?
1
. Bar-2 has diameter, 2d, length 2L, an elastic modulus 2E and subjected to
tensile load 2P, resulting in an elongation of ?
2
. Find the ratio ?
1
/ ?
2
.
Q.4 In a plane stress problem, the principal stresses at a point are 30MPa and -15MPa. At the same
point, on an element whose sides make an angle of 45
o
with respect to the principal axes, the
normal stresses (in MPa) are
(A) 15/2 and 15/2 (B) 30/2 and 30/2 (C) 15/2 and -15/2 (D) 30/2 and -30/2
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 2/8
Q.5 Two systems shown below start from rest. For the system shown on the left, two 50N blocks are
connected by a cord. For the system shown on the right, the 50N block is pulled by a 50N
downward force. Neglect friction. Which of the following is true?
(A) Blocks A and C have the same acceleration.
(B) Block C will have a larger acceleration than block A.
(C) Block A will have a larger acceleration than block C.
(D) Block A will not move.
Q.6 Two massless rigid bars, each of length a = 0.5m, are connected by a rotational spring having
stiffness k = 1000 N.m/rad. Find the buckling load P (in kN).
Q.7 A simply supported beam having a rectangular cross-section of depth d is subjected to a vertical
concentrated load P at the mid-span. The maximum shear stress in a section occurs at
(A) d/2 from the top of the cross-section
(B) d/3 from the top of the cross-section
(C) 2d/3 from the top of the cross-section
(D) Top of the cross-section
Q.8 A steel block of size 100?50?25 mm
3
is subjected to a uniform pressure on all faces. The
dimension of the 100mm edge reduces by 25?m (note 1 ?m = 10
-6
m). Find the applied pressure (in
GPa). Use E = 240 GPa and ? = 0.3.
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 3/8
Q.9 Which one of the following statements is true?
(A) In a tensile test on a rod made of ductile material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(B) In a tensile test on a rod made of brittle material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(C) In a torsion test on a rod made of ductile material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(D) In a torsion test on a rod made of brittle material, failure occurs along a plane making 0
o
with
respect to the axis of the rod
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 4/8
Q. 10 ? Q. 22 carry two marks each.
Q.10 A block is travelling with a constant speed v
o
on a smooth surface when the surface suddenly
becomes rough with a coefficient of friction ?, which causes the block to stop after a distance d.
When the block travels twice as fast, i.e. at a speed 2v
o
, it travels a distance D on the rough surface
before stopping. Find the ratio D/ d.
Q.11 The beam shown below is loaded with a concentrated clockwise moment of 80kN-m at point B.
The bending moment diagram (in kN-m) is
(A)
(B)
(C)
(D)
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GATE 2015 SOLID MECHANICS ? XE-D
XE-D 1/8
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 Find the force (in kN) in the member BH of the truss shown.
Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having side length a.
At point B, the equivalent force and couple are, respectively,
(A) F( ?) and 3 ?3Fa (clockwise)
(B) F( ?) and ?3Fa (clockwise)
(C) F( ?) and ?3Fa (counter clockwise)
(D) F( ?) and 3 ?3Fa (counter clockwise)
Q.3 Bar-1 has a diameter d, length L, and elastic modulus E and subjected to tensile load P, resulting in
an elongation of ?
1
. Bar-2 has diameter, 2d, length 2L, an elastic modulus 2E and subjected to
tensile load 2P, resulting in an elongation of ?
2
. Find the ratio ?
1
/ ?
2
.
Q.4 In a plane stress problem, the principal stresses at a point are 30MPa and -15MPa. At the same
point, on an element whose sides make an angle of 45
o
with respect to the principal axes, the
normal stresses (in MPa) are
(A) 15/2 and 15/2 (B) 30/2 and 30/2 (C) 15/2 and -15/2 (D) 30/2 and -30/2
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 2/8
Q.5 Two systems shown below start from rest. For the system shown on the left, two 50N blocks are
connected by a cord. For the system shown on the right, the 50N block is pulled by a 50N
downward force. Neglect friction. Which of the following is true?
(A) Blocks A and C have the same acceleration.
(B) Block C will have a larger acceleration than block A.
(C) Block A will have a larger acceleration than block C.
(D) Block A will not move.
Q.6 Two massless rigid bars, each of length a = 0.5m, are connected by a rotational spring having
stiffness k = 1000 N.m/rad. Find the buckling load P (in kN).
Q.7 A simply supported beam having a rectangular cross-section of depth d is subjected to a vertical
concentrated load P at the mid-span. The maximum shear stress in a section occurs at
(A) d/2 from the top of the cross-section
(B) d/3 from the top of the cross-section
(C) 2d/3 from the top of the cross-section
(D) Top of the cross-section
Q.8 A steel block of size 100?50?25 mm
3
is subjected to a uniform pressure on all faces. The
dimension of the 100mm edge reduces by 25?m (note 1 ?m = 10
-6
m). Find the applied pressure (in
GPa). Use E = 240 GPa and ? = 0.3.
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 3/8
Q.9 Which one of the following statements is true?
(A) In a tensile test on a rod made of ductile material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(B) In a tensile test on a rod made of brittle material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(C) In a torsion test on a rod made of ductile material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(D) In a torsion test on a rod made of brittle material, failure occurs along a plane making 0
o
with
respect to the axis of the rod
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 4/8
Q. 10 ? Q. 22 carry two marks each.
Q.10 A block is travelling with a constant speed v
o
on a smooth surface when the surface suddenly
becomes rough with a coefficient of friction ?, which causes the block to stop after a distance d.
When the block travels twice as fast, i.e. at a speed 2v
o
, it travels a distance D on the rough surface
before stopping. Find the ratio D/ d.
Q.11 The beam shown below is loaded with a concentrated clockwise moment of 80kN-m at point B.
The bending moment diagram (in kN-m) is
(A)
(B)
(C)
(D)
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 5/8
Q.12 The beam shown has an internal hinge at B. A vertical load P = 25kN is applied at B. Use L = 2m.
Magnitude of the reactions (i.e. forces and moments) at A and C are
(A) Vertical reaction force at C is 12.5kN, vertical reaction force at A is 12.5kN, moment reaction
at A is 0kN-m.
(B) Vertical reaction force at C is 0kN, vertical reaction force at A is 25kN, moment reaction at A
is 50kN-m.
(C) Vertical reaction force at C is 25kN, vertical reaction force at A is 0kN, moment reaction at A
is 50kN-m.
(D) Vertical reaction force at C is 0kN, vertical reaction force at A is 25kN, moment reaction at A
is 25kN-m.
Q.13 Blocks P and Q are released from rest in the positions shown. Neglect friction between all surfaces,
i.e., both blocks can translate freely. Then the direction of the acceleration of block Q (i.e. a
Q
) is
(A)
(B)
(C)
(D)
Q.14 The acceleration, a, of a particle as a function of its position, x, is given by the relation
=.+
, where a and x are expressed in m/s
2
and meters, respectively. Consider b = 1m.
When x = 0, velocity is v = 1m/s. Find v (in m/s) when x = ? meters.
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GATE 2015 SOLID MECHANICS ? XE-D
XE-D 1/8
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 Find the force (in kN) in the member BH of the truss shown.
Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having side length a.
At point B, the equivalent force and couple are, respectively,
(A) F( ?) and 3 ?3Fa (clockwise)
(B) F( ?) and ?3Fa (clockwise)
(C) F( ?) and ?3Fa (counter clockwise)
(D) F( ?) and 3 ?3Fa (counter clockwise)
Q.3 Bar-1 has a diameter d, length L, and elastic modulus E and subjected to tensile load P, resulting in
an elongation of ?
1
. Bar-2 has diameter, 2d, length 2L, an elastic modulus 2E and subjected to
tensile load 2P, resulting in an elongation of ?
2
. Find the ratio ?
1
/ ?
2
.
Q.4 In a plane stress problem, the principal stresses at a point are 30MPa and -15MPa. At the same
point, on an element whose sides make an angle of 45
o
with respect to the principal axes, the
normal stresses (in MPa) are
(A) 15/2 and 15/2 (B) 30/2 and 30/2 (C) 15/2 and -15/2 (D) 30/2 and -30/2
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 2/8
Q.5 Two systems shown below start from rest. For the system shown on the left, two 50N blocks are
connected by a cord. For the system shown on the right, the 50N block is pulled by a 50N
downward force. Neglect friction. Which of the following is true?
(A) Blocks A and C have the same acceleration.
(B) Block C will have a larger acceleration than block A.
(C) Block A will have a larger acceleration than block C.
(D) Block A will not move.
Q.6 Two massless rigid bars, each of length a = 0.5m, are connected by a rotational spring having
stiffness k = 1000 N.m/rad. Find the buckling load P (in kN).
Q.7 A simply supported beam having a rectangular cross-section of depth d is subjected to a vertical
concentrated load P at the mid-span. The maximum shear stress in a section occurs at
(A) d/2 from the top of the cross-section
(B) d/3 from the top of the cross-section
(C) 2d/3 from the top of the cross-section
(D) Top of the cross-section
Q.8 A steel block of size 100?50?25 mm
3
is subjected to a uniform pressure on all faces. The
dimension of the 100mm edge reduces by 25?m (note 1 ?m = 10
-6
m). Find the applied pressure (in
GPa). Use E = 240 GPa and ? = 0.3.
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 3/8
Q.9 Which one of the following statements is true?
(A) In a tensile test on a rod made of ductile material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(B) In a tensile test on a rod made of brittle material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(C) In a torsion test on a rod made of ductile material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(D) In a torsion test on a rod made of brittle material, failure occurs along a plane making 0
o
with
respect to the axis of the rod
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 4/8
Q. 10 ? Q. 22 carry two marks each.
Q.10 A block is travelling with a constant speed v
o
on a smooth surface when the surface suddenly
becomes rough with a coefficient of friction ?, which causes the block to stop after a distance d.
When the block travels twice as fast, i.e. at a speed 2v
o
, it travels a distance D on the rough surface
before stopping. Find the ratio D/ d.
Q.11 The beam shown below is loaded with a concentrated clockwise moment of 80kN-m at point B.
The bending moment diagram (in kN-m) is
(A)
(B)
(C)
(D)
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 5/8
Q.12 The beam shown has an internal hinge at B. A vertical load P = 25kN is applied at B. Use L = 2m.
Magnitude of the reactions (i.e. forces and moments) at A and C are
(A) Vertical reaction force at C is 12.5kN, vertical reaction force at A is 12.5kN, moment reaction
at A is 0kN-m.
(B) Vertical reaction force at C is 0kN, vertical reaction force at A is 25kN, moment reaction at A
is 50kN-m.
(C) Vertical reaction force at C is 25kN, vertical reaction force at A is 0kN, moment reaction at A
is 50kN-m.
(D) Vertical reaction force at C is 0kN, vertical reaction force at A is 25kN, moment reaction at A
is 25kN-m.
Q.13 Blocks P and Q are released from rest in the positions shown. Neglect friction between all surfaces,
i.e., both blocks can translate freely. Then the direction of the acceleration of block Q (i.e. a
Q
) is
(A)
(B)
(C)
(D)
Q.14 The acceleration, a, of a particle as a function of its position, x, is given by the relation
=.+
, where a and x are expressed in m/s
2
and meters, respectively. Consider b = 1m.
When x = 0, velocity is v = 1m/s. Find v (in m/s) when x = ? meters.
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 6/8
Q.15 The 30kg block B shown below is suspended by a 2m cord attached to the 60kg cart A. Friction is
negligible. If the system is released from rest in the position shown, find the ratio of the velocity
magnitudes
| |/| | when the cord is vertical.
Q.16 The plane frame shown has an internal hinge at C. Find the magnitude of axial force (in kN) in
member BC.
Q.17 Two 50mm diameter solid steel rods are rigidly connected together at right angles and loaded as
shown. Use P = 1000 ? kN. At point A, located at the top of the cross-section at the fixed end, the
magnitude of bending stress ( ?) and shear stress ( ?) are
(A) ? = 256 MPa, ? = 512 MPa (B) ? = 512 MPa, ? = 256 MPa
(C) ? = 512 MPa, ? = 128 MPa (D) ? = 128 MPa, ? = 512 MPa
Q.18 At a temperature of 40
o
C, a rod tightly fits between two rigid walls such that the compressive stress
in the rod is 60MPa. Given E = 200GPa and ? = 20?10
-6
/
o
C, find the temperature at which the rod
will just lose contact with the walls.
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GATE 2015 SOLID MECHANICS ? XE-D
XE-D 1/8
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 Find the force (in kN) in the member BH of the truss shown.
Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having side length a.
At point B, the equivalent force and couple are, respectively,
(A) F( ?) and 3 ?3Fa (clockwise)
(B) F( ?) and ?3Fa (clockwise)
(C) F( ?) and ?3Fa (counter clockwise)
(D) F( ?) and 3 ?3Fa (counter clockwise)
Q.3 Bar-1 has a diameter d, length L, and elastic modulus E and subjected to tensile load P, resulting in
an elongation of ?
1
. Bar-2 has diameter, 2d, length 2L, an elastic modulus 2E and subjected to
tensile load 2P, resulting in an elongation of ?
2
. Find the ratio ?
1
/ ?
2
.
Q.4 In a plane stress problem, the principal stresses at a point are 30MPa and -15MPa. At the same
point, on an element whose sides make an angle of 45
o
with respect to the principal axes, the
normal stresses (in MPa) are
(A) 15/2 and 15/2 (B) 30/2 and 30/2 (C) 15/2 and -15/2 (D) 30/2 and -30/2
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 2/8
Q.5 Two systems shown below start from rest. For the system shown on the left, two 50N blocks are
connected by a cord. For the system shown on the right, the 50N block is pulled by a 50N
downward force. Neglect friction. Which of the following is true?
(A) Blocks A and C have the same acceleration.
(B) Block C will have a larger acceleration than block A.
(C) Block A will have a larger acceleration than block C.
(D) Block A will not move.
Q.6 Two massless rigid bars, each of length a = 0.5m, are connected by a rotational spring having
stiffness k = 1000 N.m/rad. Find the buckling load P (in kN).
Q.7 A simply supported beam having a rectangular cross-section of depth d is subjected to a vertical
concentrated load P at the mid-span. The maximum shear stress in a section occurs at
(A) d/2 from the top of the cross-section
(B) d/3 from the top of the cross-section
(C) 2d/3 from the top of the cross-section
(D) Top of the cross-section
Q.8 A steel block of size 100?50?25 mm
3
is subjected to a uniform pressure on all faces. The
dimension of the 100mm edge reduces by 25?m (note 1 ?m = 10
-6
m). Find the applied pressure (in
GPa). Use E = 240 GPa and ? = 0.3.
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 3/8
Q.9 Which one of the following statements is true?
(A) In a tensile test on a rod made of ductile material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(B) In a tensile test on a rod made of brittle material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(C) In a torsion test on a rod made of ductile material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(D) In a torsion test on a rod made of brittle material, failure occurs along a plane making 0
o
with
respect to the axis of the rod
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 4/8
Q. 10 ? Q. 22 carry two marks each.
Q.10 A block is travelling with a constant speed v
o
on a smooth surface when the surface suddenly
becomes rough with a coefficient of friction ?, which causes the block to stop after a distance d.
When the block travels twice as fast, i.e. at a speed 2v
o
, it travels a distance D on the rough surface
before stopping. Find the ratio D/ d.
Q.11 The beam shown below is loaded with a concentrated clockwise moment of 80kN-m at point B.
The bending moment diagram (in kN-m) is
(A)
(B)
(C)
(D)
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 5/8
Q.12 The beam shown has an internal hinge at B. A vertical load P = 25kN is applied at B. Use L = 2m.
Magnitude of the reactions (i.e. forces and moments) at A and C are
(A) Vertical reaction force at C is 12.5kN, vertical reaction force at A is 12.5kN, moment reaction
at A is 0kN-m.
(B) Vertical reaction force at C is 0kN, vertical reaction force at A is 25kN, moment reaction at A
is 50kN-m.
(C) Vertical reaction force at C is 25kN, vertical reaction force at A is 0kN, moment reaction at A
is 50kN-m.
(D) Vertical reaction force at C is 0kN, vertical reaction force at A is 25kN, moment reaction at A
is 25kN-m.
Q.13 Blocks P and Q are released from rest in the positions shown. Neglect friction between all surfaces,
i.e., both blocks can translate freely. Then the direction of the acceleration of block Q (i.e. a
Q
) is
(A)
(B)
(C)
(D)
Q.14 The acceleration, a, of a particle as a function of its position, x, is given by the relation
=.+
, where a and x are expressed in m/s
2
and meters, respectively. Consider b = 1m.
When x = 0, velocity is v = 1m/s. Find v (in m/s) when x = ? meters.
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 6/8
Q.15 The 30kg block B shown below is suspended by a 2m cord attached to the 60kg cart A. Friction is
negligible. If the system is released from rest in the position shown, find the ratio of the velocity
magnitudes
| |/| | when the cord is vertical.
Q.16 The plane frame shown has an internal hinge at C. Find the magnitude of axial force (in kN) in
member BC.
Q.17 Two 50mm diameter solid steel rods are rigidly connected together at right angles and loaded as
shown. Use P = 1000 ? kN. At point A, located at the top of the cross-section at the fixed end, the
magnitude of bending stress ( ?) and shear stress ( ?) are
(A) ? = 256 MPa, ? = 512 MPa (B) ? = 512 MPa, ? = 256 MPa
(C) ? = 512 MPa, ? = 128 MPa (D) ? = 128 MPa, ? = 512 MPa
Q.18 At a temperature of 40
o
C, a rod tightly fits between two rigid walls such that the compressive stress
in the rod is 60MPa. Given E = 200GPa and ? = 20?10
-6
/
o
C, find the temperature at which the rod
will just lose contact with the walls.
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 7/8
Q.19 A massless rigid rod AB of length h is pinned at end A and carries mass m at end B. The rod is also
supported by two linear springs of stiffness k at a height d from the end A. Use m = 4kg, h = 0.5m,
d = 0.2m, k = 600N/m and g = 10 m/s
2
. For small oscillations about the position shown, find the
frequency of free vibration (in rad/s).
Q.20 Find the maximum force P (in kN) that can be applied to the planar structure ABC so as to prevent
buckling in any of the members. Consider buckling only in the plane of the structure. Joint B is a
pin connection. Use E = 200GPa for both members. The diameter of member AB is 10 mm and the
diameter of member BC is 15 mm.
Q.21 The plane frame shown is analyzed by neglecting axial and shear deformations. The horizontal
displacement of joint B is
(A)
(B)
(C)
(D)
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GATE 2015 SOLID MECHANICS ? XE-D
XE-D 1/8
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 Find the force (in kN) in the member BH of the truss shown.
Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having side length a.
At point B, the equivalent force and couple are, respectively,
(A) F( ?) and 3 ?3Fa (clockwise)
(B) F( ?) and ?3Fa (clockwise)
(C) F( ?) and ?3Fa (counter clockwise)
(D) F( ?) and 3 ?3Fa (counter clockwise)
Q.3 Bar-1 has a diameter d, length L, and elastic modulus E and subjected to tensile load P, resulting in
an elongation of ?
1
. Bar-2 has diameter, 2d, length 2L, an elastic modulus 2E and subjected to
tensile load 2P, resulting in an elongation of ?
2
. Find the ratio ?
1
/ ?
2
.
Q.4 In a plane stress problem, the principal stresses at a point are 30MPa and -15MPa. At the same
point, on an element whose sides make an angle of 45
o
with respect to the principal axes, the
normal stresses (in MPa) are
(A) 15/2 and 15/2 (B) 30/2 and 30/2 (C) 15/2 and -15/2 (D) 30/2 and -30/2
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 2/8
Q.5 Two systems shown below start from rest. For the system shown on the left, two 50N blocks are
connected by a cord. For the system shown on the right, the 50N block is pulled by a 50N
downward force. Neglect friction. Which of the following is true?
(A) Blocks A and C have the same acceleration.
(B) Block C will have a larger acceleration than block A.
(C) Block A will have a larger acceleration than block C.
(D) Block A will not move.
Q.6 Two massless rigid bars, each of length a = 0.5m, are connected by a rotational spring having
stiffness k = 1000 N.m/rad. Find the buckling load P (in kN).
Q.7 A simply supported beam having a rectangular cross-section of depth d is subjected to a vertical
concentrated load P at the mid-span. The maximum shear stress in a section occurs at
(A) d/2 from the top of the cross-section
(B) d/3 from the top of the cross-section
(C) 2d/3 from the top of the cross-section
(D) Top of the cross-section
Q.8 A steel block of size 100?50?25 mm
3
is subjected to a uniform pressure on all faces. The
dimension of the 100mm edge reduces by 25?m (note 1 ?m = 10
-6
m). Find the applied pressure (in
GPa). Use E = 240 GPa and ? = 0.3.
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 3/8
Q.9 Which one of the following statements is true?
(A) In a tensile test on a rod made of ductile material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(B) In a tensile test on a rod made of brittle material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(C) In a torsion test on a rod made of ductile material, failure occurs along a plane making 45
o
with
respect to the axis of the rod
(D) In a torsion test on a rod made of brittle material, failure occurs along a plane making 0
o
with
respect to the axis of the rod
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 4/8
Q. 10 ? Q. 22 carry two marks each.
Q.10 A block is travelling with a constant speed v
o
on a smooth surface when the surface suddenly
becomes rough with a coefficient of friction ?, which causes the block to stop after a distance d.
When the block travels twice as fast, i.e. at a speed 2v
o
, it travels a distance D on the rough surface
before stopping. Find the ratio D/ d.
Q.11 The beam shown below is loaded with a concentrated clockwise moment of 80kN-m at point B.
The bending moment diagram (in kN-m) is
(A)
(B)
(C)
(D)
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 5/8
Q.12 The beam shown has an internal hinge at B. A vertical load P = 25kN is applied at B. Use L = 2m.
Magnitude of the reactions (i.e. forces and moments) at A and C are
(A) Vertical reaction force at C is 12.5kN, vertical reaction force at A is 12.5kN, moment reaction
at A is 0kN-m.
(B) Vertical reaction force at C is 0kN, vertical reaction force at A is 25kN, moment reaction at A
is 50kN-m.
(C) Vertical reaction force at C is 25kN, vertical reaction force at A is 0kN, moment reaction at A
is 50kN-m.
(D) Vertical reaction force at C is 0kN, vertical reaction force at A is 25kN, moment reaction at A
is 25kN-m.
Q.13 Blocks P and Q are released from rest in the positions shown. Neglect friction between all surfaces,
i.e., both blocks can translate freely. Then the direction of the acceleration of block Q (i.e. a
Q
) is
(A)
(B)
(C)
(D)
Q.14 The acceleration, a, of a particle as a function of its position, x, is given by the relation
=.+
, where a and x are expressed in m/s
2
and meters, respectively. Consider b = 1m.
When x = 0, velocity is v = 1m/s. Find v (in m/s) when x = ? meters.
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 6/8
Q.15 The 30kg block B shown below is suspended by a 2m cord attached to the 60kg cart A. Friction is
negligible. If the system is released from rest in the position shown, find the ratio of the velocity
magnitudes
| |/| | when the cord is vertical.
Q.16 The plane frame shown has an internal hinge at C. Find the magnitude of axial force (in kN) in
member BC.
Q.17 Two 50mm diameter solid steel rods are rigidly connected together at right angles and loaded as
shown. Use P = 1000 ? kN. At point A, located at the top of the cross-section at the fixed end, the
magnitude of bending stress ( ?) and shear stress ( ?) are
(A) ? = 256 MPa, ? = 512 MPa (B) ? = 512 MPa, ? = 256 MPa
(C) ? = 512 MPa, ? = 128 MPa (D) ? = 128 MPa, ? = 512 MPa
Q.18 At a temperature of 40
o
C, a rod tightly fits between two rigid walls such that the compressive stress
in the rod is 60MPa. Given E = 200GPa and ? = 20?10
-6
/
o
C, find the temperature at which the rod
will just lose contact with the walls.
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 7/8
Q.19 A massless rigid rod AB of length h is pinned at end A and carries mass m at end B. The rod is also
supported by two linear springs of stiffness k at a height d from the end A. Use m = 4kg, h = 0.5m,
d = 0.2m, k = 600N/m and g = 10 m/s
2
. For small oscillations about the position shown, find the
frequency of free vibration (in rad/s).
Q.20 Find the maximum force P (in kN) that can be applied to the planar structure ABC so as to prevent
buckling in any of the members. Consider buckling only in the plane of the structure. Joint B is a
pin connection. Use E = 200GPa for both members. The diameter of member AB is 10 mm and the
diameter of member BC is 15 mm.
Q.21 The plane frame shown is analyzed by neglecting axial and shear deformations. The horizontal
displacement of joint B is
(A)
(B)
(C)
(D)
GATE 2015 SOLID MECHANICS ? XE-D
XE-D 8/8
Q.22 A thin walled cylindrical pressure vessel having mean radius 100mm and wall thickness 5mm, is
subjected to internal pressure p. If the factor of safety is 2 and the yield stress in shear is 100MPa,
find the maximum value of p (in MPa).
END OF THE QUESTION PAPER
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This post was last modified on 19 December 2019