If the inertial mass and gravitational mass of the simple pendulum of length l are not equal, then the time period of the simple pendulum is :

Options

A. `T= 2pi sqrt((m_(i)l)/(m_(g)g))`
B. `T= 2pi sqrt((m_(g)l)/(m_(i)g))`
C. `T=2pi (m_(g))/(m_(i)) sqrt((l)/(g))`
D. `T=2pi (m_(i))/(m_(g)) sqrt((l)/(g))`

Answer

A

Explanation

`T= 2pi sqrt((M)/(K))`
`:. T_(1)=2pi sqrt((M_(1))/(k)): T_(2)= 2pi sqrt((M_(2))/(k))`
Inertial mass `M_(1) prop m_(i) l`
Gravitational mass `M_(2) prop m_(g)g`
`:. (T_(1))/(T_(2))= 2pi sqrt((M_(2)l)/(k))xx(1)/(2pi) sqrt((k)/(m_(g)g))`
`:. T= 2pi sqrt((m_(i)l)/(m_(g)g)`