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 giv

Question

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 giv

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
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))`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - B
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))`

4 views Answered 2023-02-05 15:29