First slide

Moment of intertia

Question

If two circular discs A and B are of same mass but of radii rand 2r respectively, then the moment of inertia of A is [Kerala CEE 2015]

Easy

A

one-fourth that of B
B

twice that of B
C

four times that of B
D

same as that of B

Solution

Given, radius of circular disc $A, r_{1} = r$
Radius of circular disc $B, r_{2} = 2 r$
For disc $A, I_{A} = m r^{2}$ …(i)
For disc $B, I_{B} = m (2 r)^{2} = 4 m r^{2}$ …(ii)
On dividing Eq. (i) by Eq. (ii), we get
$∴ \frac{I_{A}}{I_{B}} = \frac{m r^{2}}{4 m r^{2}} \Rightarrow \frac{I_{A}}{I_{B}} = \frac{1}{4} \Rightarrow I_{A} = \frac{1}{4} I_{B}$
So, moment of inertia of A is one-fourth that of B.

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