Q181 / 200 · Manipal (MET) 2013 · Physics

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

Correct answer
A
$3 T$
B
$3 / 2 T$
C
$4 T$
D
$2 T$

Solution

The periodic-time of a simple pendulum is given by $\begin{aligned} T & =2 \pi \sqrt{\frac{l}{g}} \\ T_1 & =T, l_1=l, l_2=9 l \\ \frac{T_1}{T_2} & =\sqrt{\frac{l_4}{l_2}}=\sqrt{\frac{1}{9}}=\frac{1}{3} \\ T_2 & =3 T_1=3 T\end{aligned}$

Hence, the correct answer is option: 'A'.

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