Question
A solid sphere of 80 ~kg and radius 15 ~m moving in a space becomes a circular disc of radius 20 ~m in 1 ~h . The rate of change of moment of Inertia in this process is
BITSAT
Physics
Rotational Motion
2022
BITSAT 2022
BITSAT Physics Question (2022) — Solution
Options
- A. 30 9 ~kg ^2 ~m ^2 ~s ^ -1
- B. 25 9 ~kg ^ - m ^2 ~s ^ -1
- C. 10 9 ~kg - m ^2 ~s ^ -1
- D. 22 9 ~kg ^ - m ^2 ~s ^ -1
Answer
D. 22 9 ~kg ^ - m ^2 ~s ^ -1
Step-by-step solution
Given, mass of solid sphere =80 ~kg radius of solid sphere, R_s=15 ~m radius of circular disc, R_c=20 ~m and time =1 hour =60 minute =60 60 sec Moment of inertia of solid sphere, I_s= 2 5 M R^2 aligned & = 2 5 80 (15)^2 \\ & =7200 ~kg - m ^2 aligned Similarly, moment of inertia of the disc, aligned I_c & = 1 2 M R_c^2 \\ & = 1 2 80 (20)^2 \\ & =16000 ~kg - m ^2 aligned aligned Rate of change of moment of Inertia & = I_c-I_s t \\ & = 16000-7200 60 60 \\ & = 22 9 ~kg - m ^2 ~s ^ -1 aligned
Related: Physics — Rotational Motion · All PYQ Banks