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The mass and diameter of a planet are tw...

The mass and diameter of a planet are twice those of earth. What will be the period of oscillation of a pendulum on this plenet. If it is a 2 second's pendulum on earth?

A

`(1)/(sqrt(2))` s

B

`2 sqrt(2) s`

C

2s

D

`(1)/(2) s`

Text Solution

Verified by Experts

The correct Answer is:
B
Since, acceleration due to gravity
`g = (GM)/( R^(2)) rArr (g_(e))/( g_(P)) = (M_(e))/(M_(P)) xx (R_(P)^(2))/(R_(e)^(2))`
`rArr (g_(e))/( g_(P)) = (2)/(1) rArr g_(P) = (g_(e))/(2) = (g)/(2)`
Since , `T prop (1)/( sqrt(g))`
`rArr (T_(e))/(T_(P)) = sqrt((g_(P))/(g_(e))) rArr (2)/(T_(P)) = sqrt((T)/(2)) rArr T_(P) = 2 sqrt( 2)` sec
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