The length of a second's pendulum is 1 m on the earth. If the mass and diameter of a planet than that of earth, then the length of the second's pendulum on the planet will be

Options

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

Answer

D

Explanation

For a second's pendulum, T = 2s
`therefore 2 = 2pi sqrt((l)/(g))` on the surface of the earth `" "` …….(1)
On the planet `2=2pi sqrt((l')/(g'))" "` …….(2)
`therefore (l)/(g)=(l')/(g') " " therefore " "l'=l((g')/(g))" "`......(3)
But `g=(GM)/(R^(2)) " " therefore " " (g')/(g)=(GM')/(R'^(2))xx(R^(2))/(GM)" "`
`= 2xx((1)/(2))^(2)=(1)/(2)" "` .....(4)
`therefore l'=l xx (1)/(2)=(1)/(2)m = 0.5 m`