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Question 1:A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, t = 0. It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is 10 m/s^{2} and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of

[2018]

Question 2:A rigid link PQ is undergoing plane motion as shown in the figure (V_{p} and V_{Q} are non-zero). V_{QP} is the relative velocity of point Q with respect to point P.

Which one of the following is TRUE?

Which one of the following is TRUE?

[2016]

Question 3:A circular object of radius /rolls without slipping on a horizontal level floor with the center having velocity V. The velocity at the point of contact between the object and the floor is

[2014]

Question 4:A straight rod length L(t), hinged at one end freely extensible at the other end, rotates through an angle θ(t) about the hinge. At time t, L(t) = 1 m, L(t) = 1 m/s, θ(t) = p/4 rad and θ (t) = 1 rad/s.

The magnitude of the velocity at the other end of the rod is

The magnitude of the velocity at the other end of the rod is

[2008]

Question 5:A reel of mass m and radius of gyration k is rolling down smoothly from rest with one end of the thread wound on it held in the ceiling as depicted in the figure.

Consider the thickness of the thread and its mass negligible in comparison with the radius r of the hub and the reel mass m. Symbol g represents the acceleration due to gravity.

The tension in the thread is

Consider the thickness of the thread and its mass negligible in comparison with the radius r of the hub and the reel mass m. Symbol g represents the acceleration due to gravity.

The tension in the thread is

[2003]

Question 6:A shell is fired from a cannon. At the instant the shell is just about to leave the barrel, its velocity relative to the barrel is 3 m/s, while the barrel is swinging upwards with a constant angular velocity of 2 rad/s. The magnitude of the absolute velocity of the shell is

[2005]

Question 7:A reel of mass m and radius of gyration k is rolling down smoothly from rest with one end of the thread wound on it held in the ceiling as depicted in the figure.

Consider the thickness of the thread and its mass negligible in comparison with the radius r of the hub and the reel mass m. Symbol g represents the acceleration due to gravity.

The linear acceleration of the reel is

Consider the thickness of the thread and its mass negligible in comparison with the radius r of the hub and the reel mass m. Symbol g represents the acceleration due to gravity.

The linear acceleration of the reel is

[2003]

Question 8:Instantaneous centre of a body rolling without sliding on a stationary curved surface lies.

[1992]

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