Question 636: Centre of Mass and Rotational Motion

Question

Three objects, A : (a solid sphere), B : (a thin
circular disk) and C : (a circular ring), each
have the same mass M and radius R. They
all spin with the same angular speed $$\omega $$ about
their own symmetry axes. The amounts of
work (W) required to bring them to rest, would
satisfy the relation

Accepted Answer

Work done required to bring them rest
$$\Delta $$W = $$\Delta $$K
E
(work-energy theorem)
$$\Delta $$W = $${1 \over 2}I{\omega ^2}$$
For same $$\omega $$, $$\Delta $$W $$\infty $$ I
For a solid sphere, I
A
= $${2 \over 5}M{R^2}$$
For a thin circular disk, I
B
= $${1 \over 2}M{R^2}$$
For a circular ring, I
C
= MR
2
$$ 	herefore $$ I
C
> I
B
> I
A
So, W
C
> W
B
> W
A

Answer

WC > WB > WA

Answer

WA > WB > WC

Answer

WB > WA > WC

Answer

WA > WC > WB

Centre of Mass and Rotational Motion

Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed $\omega $ about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

Choose the correct answer: