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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 13715MR2Step 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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