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Question

Let 'M' be the mass and 'L' be the length of a thin uniform rod. In first case, axis of rotation is passing through centre and perpendicular to the length of the rod. In second case axis of rotation is passing through one end and perpendicular to the length of the rod. The ratio of radius of gyration in first case to second case is

A
1
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B
12
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C
14
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D
18
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Solution

The correct option is A 12
Moment of inertia of the rod about an axis passing through its centre and perpendicular to the length I1=112ML2
Using Mk21=I1=112ML2
We get radius of gyration k1=L12
Moment of inertia of the rod about an axis passing through its one end and perpendicular to the length I2=13ML2
Using Mk22=I2=13ML2
We get radius of gyration k2=L3
Thus ratio of radius of gyration k1k2=L/12L/3
k1k2=12

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