Question

A thin, very light wire is wrapped around a drum that is free to rotate, the free end of the wire is attached to a ball of mass m, the drum is initially a solid disk with a mass M and radius R. you let the mass go at height h above the ground. if you switch out the solid disk and use a hollow disk instead with the same mass and radius, how will the final speed when the mass hits the ground when using a hollow disk compare to the final speed when using a solid disk?

a-greater than the original
b-less than the original
c-cant be determined
d-same as the original

Answer 1

a-greater than the original (solid disk)

Step-by-step explanation:

The hollow drum's lower rotational inertia allows it to rotate faster as the wire unwinds. This absorbs more potential energy, leaving less to translate into the speed of the falling mass. Therefore, the final speed when using a hollow disk will be:

a-greater than the original (solid disk)