A simple pendulum has a time period `T_(1)` on the surface of earth of radius R. When taken to a height of R above the earth's surface, its time period is `T_(2)`, ratio `(T_(2))/(T)` is

Options

A. `(1)/(sqrt(2))`
B. `sqrt(2)`
C. 2
D. 4

Answer

C

Explanation

`(T_(1))/(T_(2))=sqrt((g_(2))/(g_(1)))`
`g_(1)=g,g_(2)=(g)/([1+(h)/(R)]^(2))`
h = R, we get
`g_(2)=(g)/(4)implies(T_(1))/(T_(2))=sqrt((g)/(4g))`
`implies (T_(2))/(T_(1))=(2)/(1)`