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 diameters
B)A disc about 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 $I _{\text {ring }}=\frac{1}{4} M R^2$
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 smallest.
BETA
