Question 22: Centre of Mass and Rotational Motion

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 .......

Accepted Answer

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 $$	imes$$ 60 sec
$$	herefore$$ Moment of inertia of solid sphere, I
s
= $$\frac{2}{5}$$ MR
2
= $$\frac{2}{5}$$ $$	imes$$ 80 $$	imes$$ (15)
2
= 7200 kg-m
2
Similarly,
moment of inertia of the disc, I
c
= $$\frac{1}{2}$$ MR$$_c^2$$
= $$\frac{1}{2}$$ $$	imes$$ 80 $$	imes$$ (20)
2
= 16000 kg-m
2
Rate of change of moment of Inertia $$ = {{{I_c} - {I_s}} \over t}$$
$$ = {{16000 - 7200} \over {60 	imes 60}}$$
= $$\frac{22}{9}$$ kg-m
2
s
$$-$$1

Answer

$$\frac{30}{9}$$ kg-m2s$$-$$1

Answer

$$\frac{25}{9}$$ kg-m2s$$-$$1

Answer

$$\frac{10}{9}$$ kg-m2s$$-$$1

Answer

$$\frac{22}{9}$$ kg-m2s$$-$$1

Centre of Mass and Rotational Motion

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 .......

Choose the correct answer: