The length of second pendulums is 1 m on earth . If mass and diameter of the planet is doubled than that or earth length becomes :

Options

A. 2 m
B. `0.5 m`
C. 4 m
D. 1 m

Answer

B

Explanation

Time period of a second pendulum is 2s.
When second pendulum is on earth then
`T= 2pi sqrt((l)/(g))`
(or) `2= 2pi sqrt((R^(2)l)/(GM)) " "....(1)`
When second pendulum is on the planet then
`=2pi sqrt(((2R)^(2)xxl')/(G(2M)))`
`=2pi sqrt((2R^(2) l')/(GM)) " "...(2)`
From (1) and (2) we get `sqrt(2l')= sqrt(l)`
(or) `l'=(1)/(2)=(1)/(2)=0.5 m`.