A solid sphere of 100 kg and radius 10 m moving in a space becomes a circular disc of radius 20 m in one hour. Then the rate of change of moment of inertia in the process is

Options

A. `40/9 kgm^2s^-1`
B. `10/9 kg m^2 s^-1`
C. `50/9 kg m^2 s^-1`
D. `25/9 kg m^2 s^-1`

Explanation

Given, mass of solid sphere `M_s=100 kg`
radius of solid sphere `R_s=10 m`
radius of circular disc `R_c= 20 m`
and time =1 hour=60 minute=`60 times 60 sec`
Moment of inertia of the solid sphere,
`I_s=2/5M_sR_s^2=2/5 times100 times(10)^2=4000 kg.m^2`
Similarly,
moment of inertia of the disc `I_c=1/2M_cR^2`
`=1/2 times100 times(20)^2=20,000 kg.m^2`
Rate of change of moment of inertia `=(I_c-I_s)/t`
`=(20000-4000)/(60 times60)=16000/(60 times60)=160/36`
`=40/9 kg.m^2s^-1`