Question

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 :

• A. $ 3T $
• B. $ 3/2T $
• C. $ 4T $
• D. $ 2T $

Answer 1

Answer: (A)

Time period $T=2 \pi \sqrt{\frac{l}{g}}$
i.e., time period does not depend on the mass of the bob.
$\therefore T \propto \sqrt{l}$
$\frac{T_{1}}{T_{2}}=\sqrt{\frac{l_{1}}{l_{2}}}$
$\Rightarrow \frac{T}{T_{2}}=\sqrt{\frac{l}{9 l}}$
$\therefore T_{2}=3 T$