Question

A horizontal disc rotating about a vertical
axis, passing through its centre makes 100
revolutions per minute. A small piece of
wax of mass 10g falls vertically on the
disc and adheres to it at a distance of 9cm.
from the axis. If the number of revolutions
per minute is thereby reduced to 90,
calculate the M.O.I. of the disc.​

Answer 1

Answer:

The moment of inertia of the disc is 2mr²

Explanation:

Let I be the moment of inertia of disc

moment of inertia of wax = mr²

after wax falls the net moment of inertia = I + mr²

Since there is no external torque acting on the system, So the angular momentum of the system will remain constant.

=> Iω = ω₁(I + mr²)

=> I x 90 = 60(I + mr²)

=> 1.5 I = I + mr²

=> 0.5 I = mr²

=> I = 2mr²

Hence the moment of inertia of the disc is 2mr2