Question

A simple pendulum has a timenperiod t in vaccum . Its time period when it is completely immersed in a liquid of density 1/8 of tge density of material of bob is

Answer 1

In vacuum, T = 2\pi\sqrt{\frac{l}{g}}

Let V be the volume and T be the desity of the mass of the bob.

Net downward force acting on the bob inside the liquid

= weight - upthrust = Vpg -V\frac{T}{8}g = \frac{7}{8}Vpg

So, time period of the bob inside the liquid

\therefore T_{1} = 2\pi\sqrt{\frac{l}{\frac{7}{8}g}} = 2\pi\sqrt{\frac{l}{g}} \times \sqrt{\frac{8}{7}} = \sqrt{\frac{8}{7}} T

Time period of pendulum in a liquid -

T= 2\pi \sqrt{\frac{l}{g\left ( 1-\frac{\rho }{\sigma } \right )}}

- wherein

\rho = density of liquid

\sigma = density of bob

l= length of pendulum.

Option 1)

\sqrt{\frac{7}{8}}T

This is incorrect.

Option 2)

\sqrt{\frac{5}{8}}T

This is incorrect.

Option 3)

\sqrt{\frac{3}{8}}T

This is incorrect.

Option 4)

\sqrt{\frac{8}{7}}T

This is correct