A simple pendulum has a 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. `sqrt(2)`
B. 1
C. 2
D. `(1)/(2)`

Answer

C

Explanation

`T_(1)=2pi sqrt((l)/(g)), g'=(g)/((1+(R )/(R ))^(2))=(g)/(4)`
`therefore T_(2)=2pi sqrt((4l)/(g))" " therefore (T_(2))/(T_(1))=sqrt((4l)/(g)xx(g)/(l))= 2`