Rotational Motion Question 124
Question: Which of the following has the highest moment of inertia when each of them has the same mass and the same radius?
Options:
A) A ring about any of its diameter
B)A disc about any of its diameter
C)A hollow sphere about any of its diameter
D)A solid sphere about any of its diameter
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Let $M$ and $R$ be the mass and radius respectively.
Moment of inertia of a ring about any of its diameter is $I _{\text {ring }}=\frac{1}{2} M R^2$
Moment of inertia of a disc about any of its diameter is $I _{\text {disc }}=\frac{1}{4} M R^2$
Moment of inertia of a hollow sphere about any of its diameter is $I _{\text {hollow sphere }}=\frac{2}{3} M R^2$
Moment of inertia of a solid sphere about any of its diameter is $I _{\text {solid sphere }}=\frac{2}{5} M R^2$
Thus. $I _{\text {hollow sphere }}$ is largest.
