A mass
m is attached to a pulley through a cord as shown in the figure. The pulley is a solid disk with radius
R. The cord does not slip on the disk. The mass is released from rest at a height
h from the ground and at the instant the mass reaches the ground, the disk is rotating with angular velocity
ω. The mass of the disk is
M=xm(2ghR2ω2−1). Find
x.