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Question

Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is:
1334214_bee7ec6ec5c24a0f81fe256f36e97753.png


A
15215MR2
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B
1715MR2
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C
13715MR2
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D
20915MR2
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Solution

The correct option is A $$\dfrac{137}{15} MR^2$$
For Ball 
using parallel axis theorem.

$$I_{ball} = \dfrac{2}{5} MR^2 + M(2R)^2$$

$$= \dfrac{22}{5} MR^2$$

2 Balls so $$\dfrac{44}{5} MR^2$$

Irod = for rod $$\dfrac{M(2R)^2}{R} = \dfrac{MR^2}{3}$$

$$I_{system} = I_{Ball} + I_{rod}$$

$$= \dfrac{44}{5} MR^2 + \dfrac{MR^2}{3}$$

$$= \dfrac{137}{15} MR^2$$

Physics

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