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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

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

The correct option is A 13715MR2
Step 1:Draw diagram of the given problem
Step 2: Calculate moment of inertia of the balls and rod.
Given,
Mass of the identical spherical balls = M
Radius of the ball =R
Length of the rod =2R
Mass of the rod =M
Here, given that L=2R
For I of the ball, using parallel axis
theorem.
Iball=25MR2+M(2R)2=225MR2

Considering both spheres at equal
distance from the axis, moment of inertia due to both spheres about this axis will be

2Iball=2×225MR2
Moment of inertia of both the ball,
Iballs=445MR2
Moment of inertia of the rod, Irod
(M(2R)2)12=(MR2)3
Step 3:Calculate moment of inertia of the system.
Isystem=Iballs+Irod
I=445MR2+(MR2)3=13715MR2
Final Answer: (c)

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