A simple pendulum with iron bob has a time period $T$. The bob is now immersed in a non-viscous liquid and oscillated. If the density of liquid is $\frac{1}{12}$ th that of iron, then new time period will be
Medium
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(c)
When bob is inserted, in liquid effective of is reduced because of the force of upthrust.
$\rho_s$ is density of solid.
$\rho_L$ is density of liquid.
$V$ is volume of solid
and $T=2 \pi \sqrt{\frac{1}{g}}$
$T_{\text {new }}=2 \pi \sqrt{\frac{1}{g_{\text {new }}}}$
$T_{\text {new }}=2 \pi \sqrt{\frac{1}{g-\frac{\rho_L}{\rho_S} g}}$
$T_{\text {new }}=2 \pi \sqrt{\frac{1 \times 12}{g \times 11}}$
or $T_{\text {new }}=\sqrt{\frac{12}{11}} T$
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