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Let M be the mass and L be the length of...

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

B

`(1)/(2)`

C

`(1)/(4)`

D

`(1)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
B
`I_(c)=(ML^(2))/(12)`
`K_(c)=(L)/(sqrt(12))`
`I_(e)=(ml^(2))/(3)`
`K_(e)=(1)/(sqrt(3))`
`(K_(c))/(K_(e))=(L)/(sqrt(12))xx(sqrt3)/(L)=(1)/(2)`.
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