Question

# The moment of inertia of a solid cylinder about its natural axis is I. If its moment of inertia about an axis perpendicular to natural axis of cylinder and passing through one end of cylinder is 196I then the ratio of radius of cylinder and its length is:

A
1:2
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B
1:3
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C
1:4
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D
2:3
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Solution

## The correct option is A 1:2The moment of inertia of a solid cylinder about its natural axis is I=mr2 ..(1)Moment of inertia about an axis perpendicular to natural axis of cylinder and passing through one end of cylinder is I1=19I6=mr24+ml23...(2)From 1 and 2 , we get 4r2=l2⇒rl=1:2

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