Question

Two simple pendulums A and B have equal lengths. The mass of bob B is three times that of bob A. Calculate the ratio of their time periods.

Answer 1

Step 1:Given data

Length of a simple pendulum of A and B$=L$

Let the mass of bob A$=x$

The mass of bob B$=$Three times of bob A

Therefore mass of bob B$=3x$

Step 2:Time period(T) formula

Time period of a simple pendulum is given as,

$$\begin{gathered} T=2\pi \sqrt{\frac{L}{g}} \\ where,L=effectivelengthofapendulum \\ g=accelerationduetogravity \\ valueofg=9.8m/s^2 \end{gathered}$$

Step 3:The ratio of their time periods

The time period of a simple pendulum does not depend on the mass of the bob.
For a given place, g is constant, the weight of the bob varies because of mass only.

So ratio of their time periods will be 1:1.

Hence, the ratio of their time periods is 1:1.