A block of mass `m` is attached to a pulley disc of equal mass, radius `r` by means of a slack string as shown. The pulley is hinged about its centre on a horizontal table and the block is projected with an initial velocity of `5 m//s`. Find the velocity when the string becomes taut.
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A block of mass m is attached to one end of a light string which is wrapped on a disc of mass 2m and radius R. The total length of the slack portion of the string is 1. The block is released from rest. The angular velocity of the disc just after the string becomes taut is

A block of mass m is attached to one end of a light string which is wrapped on a disc of mass 2m and radius R. The total length of the slack portion of the string is l . The block is released from rest. The angular velocity of the disc just after the string becomes taut is

A uniform cubical block of mass M is attached to a pulley. One end of a string, passing over the pulley is fixed to a light pole while is fixed on the bigger block and its another end is attached to a block of mass m as shown in figure. The maximum value of the mass m so that the block does not topple is : (string and pulley are ideal)

A uniform cubical block of mass M is attached to a pulley. One end of a string, passing over the pulley is fixed to a light pole while is fixed on the bigger block and its another end is attached to a block of mass m as shown in figure. The maximum value of the mass m so that the block does not topple is : (string and pulley are ideal)

Two blocks A and B are joined by means of a slacked string passing over a massless pulley as shown in Figure. The system is released from rest and it becomes taut when B falls a distance 0.5 m . a. Find the common velocity of the two blocks just after the string becomes taut. b. Find the magnitude of impulse on the pulley by the clamp during the small interval while string becomes taut.

A block is connected to a disc pulley of same mass m radius R. If the acceleration of the block is (2g)/(Z) , find Z.

A particle A of mass 2m is held on a smooth horizontal table and is attached to one end of an inelastic string which runs over a smooth light pulley at the edge of the table. At the other end of the string there hangs another particle B of mass m, the distance from A to the pulley is l. The particle A is then projected towards the pulley with velocity u. (a) Find the time before the string becomes taut, and shown that after the string becomes taut, the initial velocity of A and B is 4u//3 . (b) Find the common velocity when A reaches the pulley (assume that B has not yet reached the ground).