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GATE CE 2022: Engineering Mechanics & Design of Steel Structures#4

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Question 1

A plate of mass m and radius r slips on a rough horizontal plane. At some instant it has translation velocity V and rotational velocity V/3r. The translation velocity after the plate start pure rolling is

Question 2

A thin circular ring of mass 5 kg and radius 20 cm is rotating about its axis with an angular speed 10 rad/s. Two particles having mass 0.5 kg each are now attached at diametrically opposite points. The angular speed of the ring will be ____________rad s-1.

Question 3

The 2 kg mass C moving horizontally to the right, with a velocity of 5 m/s, strikes the 8 kg mass B at the lower end of the rigid massless rod AB. The rod is suspended from a frictionless hinge at A and is initially at rest. If the coefficient of restitution between mass C and mass B is one, determine the angular velocity of the rod AB immediately after impact.

Question 4

A rigid link PQ of length 2m rotate about the pinned end Q with a constant angular acceleration of 12 . If the acceleration of point P is 40 , the angular velocity  of link is  –

Question 5

A ball of mass 0.1 kg, initially at rest, is dropped from height of 1m. Ball hits the ground and bounces off the ground. Upon impact with the ground, the velocity reduces by 20%. The height (in m) to which the ball will rise is ___________

Question 6

In the figure shown, all surface are smooth and force constant of spring is 10 N/m. Block of mass 2 kg is not attached with the spring. The spring is compressed by 2m and then released. Find the maximum distance (in m) travelled by the block over the inclined plane. Take g = 10 m/s2

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