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  4. 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

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Q. 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

ManipalManipal 2013

Solution:

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