Question

A block is suspended by a rope that is wrapped around a massive pulley. The pulley has two spherical masses attached to its rotational axis. The mass is dropped from rest (configuration A: Left). The two masses attached to the rotational axis of the pulley are moved closer to the rotational axis and the experiment is repeated (configuration B: right). which configuration results in the block taking less time to land on the table?

Answer 1

The above problem is based on rotation of pulley and time taken by block to land on table depends on moment of inertia of pulley as explained below...
Solution In the given System when block of mass is released from given height then it moves with Constant acceleration and masive pulley rotates with Constant angular acceleration due to Torque applied by Tension in the string. Now time taken by block to land on the table depends on moment of mertia of massive pulley which changes in . 2nd Configuration as explained below. Here m = my block . And that - As shown in first Configuration, different forus are acting on block as well as pulley Now, mg-T=ma. - TR = I x - 2 I = moment of Ihertia I of bulley about a = Rx - Central axis & Put value of I in eo mg - IX = mang = mat 7 la I T = Tension in string!.

mg = of materials So using equation of motion for block :- -h=oft) + 1/ 4 (-a) +2 h = fa t2 - As time taken by block to land the table is proportional to I. So, when I increases t also increases In Configuration and Spheres spheres move clos due to which their distance from Centre deci and moment of thertia I of bulley decreases So, In Configuration and block takes less tim tre decrease