A simple pendulam has time period `T_(1)` when on the earth's surface and `T_(2)` when taken to a height `R` above the earth's surface where `R` is the radius of the earth. The value of `(T_(2))/(T_(1))` is-

Options

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

Answer

D

Explanation

For a simple pendulum
`T = 2pi sqrt((l)/(g)) therefore (T_(2))/(T_(1)) = sqrt((g_(1))/(g_(2)))`
Now, `g_(1) = (GM)/(R^(2)), g_(2) = (GM)/((2R)^(2)) = (GM)/(4R^(2))`
`therefore (T_(2))/(T_(1)) =(2)/(1)`