A simple pendulum has a length I. The inertial and gravitational masses of the bob are `m_(i) and m_(g)`, respectively. Then, the time period T is given by

Options

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

Answer

B

Explanation

Torque acting on the bob `= l alpha = - (mg)l sin theta`
or `(m_(1)l^(2))alpha = - (m_(g)g)l theta" "[because sin theta = theta]`
or `alpha = - ((m_(g)g)/(m_(i)l))theta = - omega^(2)theta`
where, `omega^(2) = (m_(g)g)/(m_(i)l)T=(2pi)/(omega)=2pi sqrt((m_(i)l)/(m_(g)g))`