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If the length of a pendulum is made 9 times and mass of the bob is made 4 times, then the value of time period becomes :
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The correct answer is:
$3 T$
Time period $T=2 \pi \sqrt{\frac{l}{g}}$
i.e., time period does not depend on the mass of the bob.
$\begin{aligned} \therefore & & T & \propto \sqrt{l} \\ & & \frac{T_1}{T_2} & =\sqrt{\frac{l_1}{l_2}} \\ & & \frac{T}{T_2} & =\sqrt{\frac{l}{9 l}} \\ & \therefore & T_2 & =3 T\end{aligned}$
i.e., time period does not depend on the mass of the bob.
$\begin{aligned} \therefore & & T & \propto \sqrt{l} \\ & & \frac{T_1}{T_2} & =\sqrt{\frac{l_1}{l_2}} \\ & & \frac{T}{T_2} & =\sqrt{\frac{l}{9 l}} \\ & \therefore & T_2 & =3 T\end{aligned}$
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