Question 634: 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

W
C
> W
B
> W
A

Answer

W
A
> W
B
> W
C

Answer

W
B
> W
A
> W
C

Answer

W
A
> W
C
> W
B

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: