Question

A hollow sphere of simple pendulum is first
filled with mercury and then with water. The
time periods are in the ratio if their densities are
in th ratio 13.6:1
pyl: 1 2) 1:2 3) 1: 13.6 4) 13.6:1​

Answer 1

Answer:

Answer is 1 ratio 1

Explanation:

2*pi*sqrt(L/g) by using this formula we get the answer as 1 ratio 1

Answer 2

Given:

A hollow sphere of simple pendulum is first filled with mercury and then with water.

To find:

Ratio of time periods if the density ratio is 13.6 : 1?

Calculation:

The general expression for time period of simple pendulum:

$\rm \therefore \: T = 2\pi \sqrt{ \dfrac{l}{g} }$

Since , the weight or density of the material in the bob is not in the expression , it will not effect the time period.

So, both water filled bob or mercury filled bob will give same time period.

So, ratio will be :

$\boxed{ \bf \therefore \: T_{mercury} : T_{water} = 1 : 1}$

Other factors on which time period will depend:

• Length of the COM of bob from hanging point (denoted as 'l' in the equation).

• Gravitational acceleration in that place (denoted as 'g).