Question

A simple pendulum with a brass bob has a time period T. The bod is now immersed in a non viscous liquid and oscillated. If the density of the liquid is 1/8 that of brass, the time period of the same pendulum will be

• A. $\sqrt{\frac{8}{7}}T$
• B. $\frac{8}{7}T$
• C. $\frac{8^2}{7}T$
• D. T

Answer 1

The correct option is A $\sqrt{\frac{8}{7}}T$

Due to buoyancy, the effective acceleration due to gravity decreases from g to $g^{\prime }=g-g/8=7g/8.SinceT=2\pi \sqrt{\frac{l}{g}}.$
The new time period will be
$T^{\prime }=2\pi \sqrt{\frac{l}{g^{\prime }}}=2\pi \sqrt{\frac{l}{7g/8}}Thus\frac{T^{\prime }}{T}=\sqrt{\frac{g}{7g/8}}=\sqrt{\frac{8}{7}}T.$
Hence the correct choice is (a).