GATE XE Mechanics of rigid bodies PYQs & Answers — Page 6

Questions 51–60 of 72. Imported answers require independent review unless marked reviewed.

A particle of mass

kg is released from rest and falls under gravity through a height of

m directly onto an upright massless elastic bar of length

mm, Young’s modulus 200 GPa, and cross-sectional area 100 mm

. Assume the following during impact: (a) particle mass sticks to the bar, (b) the bar does not buckle, and (c) no energy is lost. Use gravitational acceleration

m/s

. The maximum axial compression (in mm) of the bar due to the impact (rounded off to two decimal places) is _____.

Diagram for Engineering Sciences question 17

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A pin-jointed truss has a pin support at A and a roller support at C. All the members are made of same material and have the same cross-section. Neglect the self-weight of the members. Due to the applied loading shown, the total number of zero force members is _____.

Diagram for Engineering Sciences question 18

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The frame comprises members ABC, CD, and BEDF. This frame is fixed at A, and the connections between the three members are pins. Load P is applied at F. Which of the following statements is TRUE?

Diagram for Engineering Sciences question 3

Your answerChoose one option.

ABC and CD are two-force members

CD is the only two-force member

BEDF and CD are two-force members

ABC is the only two-force member

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When two spheres moving in a horizontal plane collide obliquely, which one of the following statements is ALWAYS TRUE?

Your answerChoose one option.

Energy of the two-sphere system is conserved

Linear momentum of the two-sphere system is conserved along the normal to the plane of impact

Linear momentum of each individual sphere is conserved along the normal to the plane of impact

Linear momentum of each individual sphere is NOT conserved along the horizontal tangent to the plane of impact

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A massless rod of length L having a concentrated mass m attached at its mid-point is held at rest between the smooth ground and the smooth wall when it makes an acute angle θ₀ with the ground as shown. The rod is then released. The acceleration due to gravity is g. At an instant when the angle between the rod and ground is θ, the velocity of the mass m is

Diagram for Engineering Sciences question 10

Your answerChoose one option.

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The block of mass m = 10 kg is held in place along the incline by the force F applied via a pulley arrangement as shown. The coefficient of static friction between the block and incline is 0.65. The range of F (in N) for which the block will remain at rest is (use acceleration due to gravity g = 10 m/s²)

Diagram for Engineering Sciences question 12

Your answerChoose one option.

6.3 to 106.30

0 to 106.30

0 to 53.15

53.15 to 106.30

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The frame shown comprises members ABC, BE, BF, and DEF. It is pin supported at A and D. Members BE and BF are pin connected to ABC and DEF. The vertical load P is applied at C. The force in the member BF is

Diagram for Engineering Sciences question 13

Your answerChoose one option.

compressive P

tensile P

compressive 2P

tensile 2P

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The slotted arm AB rotates in the horizontal plane about point A at a constant angular speed ω = 10 rad/sec. The particle P is released from rest, in the frictionless slot, at a distance of 2 m from A. The magnitude of the velocity of the particle (in m/s) just before it hits end B is ________ (rounded off to two decimal places).

Diagram for Engineering Sciences question 20

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A rigid and thin L-shaped bracket is fixed to the wall at point

, and a force

is applied at point

as shown. For a given force

, the point

experiences the maximum clockwise moment when the inclination

(in degrees) with the

-axis is .......... [up to two decimal places]

Diagram for Engineering Sciences question 6

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A horizontal effort

is applied to raise a block of weight

on a rough surface inclined at an angle

with the horizontal. If

is the coefficient of static friction between the block and the surface, the minimum effort

required to impend the upward motion of the block along the surface is

Diagram for Engineering Sciences question 11

Your answerChoose one option.

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GATE XE Mechanics of rigid bodies PYQs

Question 17

Question 18

Question 3

Question 4

Question 10

Question 12

Question 13

Question 20

Question 6

Question 11