Question

Two pulleys, one with a radius 2R and one with a radius of R, are welded together and can rotate about the same axis. A block is suspended from a string that is wrapped around the small disk and unwinds without slipping as the block descends a distance H and reaches a certain final speed. If the string with the block at the other end were wrapped around the larger disk, how would the final speed of the block change?

Answer 1

speed will double

Step-by-step explanation:

Tangential velocity is given by

v=wr

where r is radius and w is rotational velocity. When r is increased to 2R, keeping roational velocity constant, the tangential velocity doubles. Hence unwinding will take place at a twice the rate and the final velocity will be double