The length of a second's pendulum on the surface of Earth in 1m. What will be the length of a second's pendulum on the moon?

Options

A. `(1)/(6)`m
B. 1m
C. `(1)/(36)m`
D. 36 m

Answer

A

Explanation

Time period of seconds pendulum is 2s.
`therefore2=2pisqrt((L)/(g))`
On earth, `L=1m,g=g_(e)`
`therefore2=2pisqrt((1)/(g_(e)))` . . . (i)
On moon, `L=L',g=(g_(e))/(6)`
`therefore2=2pisqrt((L')/(g_(e)//6))=2pisqrt((6L')/(g_(e)))` . . . (ii)
From (i) and (ii), we get
`6L'=1` or `L'=(1)/(6)m`