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Simple Pendulum

If the length...

Question

If the length of a pendulum is made $9$ times and mass of bob is made $4$ times, then the value of time period becomes.

A

3

T

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B

3 / 2

T

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C

4

T

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D

2

T

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Solution

The correct option is A $3$ T
The periodic-time of a simple pendulum is given by
$T = 2 π \sqrt{\frac{l}{g}}$
$T_{1} = T, l_{1} = l, l_{1} = 9 l$
$\frac{T_{1}}{T_{2}} = \sqrt{\frac{l_{1}}{l_{2}}} = \sqrt{\frac{1}{9}} = \frac{1}{3}$
$T_{2} = 3 T_{1} = 3 T$ .

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