If the mass of the bob of a pendulum is increased, then the frequency of the pendulum will:

CONCEPT:

Simple pendulum:

• When a point mass is attached to an inextensible string and suspended from fixed support then it is called a simple pendulum.
• The time period of a simple pendulum is defined as the time taken by the pendulum to finish one complete oscillation.

\(⇒ T = 2\pi\sqrt{\frac{l}{g}}\)

• The above formula is only valid for small angular displacements.

Where, T = Time period of oscillation, l = length of the pendulum, and g = gravitational acceleration 

• Frequency of simple pendulum is the number of complete cycles in unit time.

\(\Rightarrow f=\frac{1}{T}\)

• The length of a simple pendulum is defined as the distance between the point of suspension to the center of the bob.

CALCULATION:

The frequency of the simple pendulum is given as,

\(\Rightarrow f=\frac{1}{2\pi}\sqrt{\frac{g}{l}}\)     -----(1)

• By equation 1 it is clear that the frequency of a simple pendulum depends on the length and the gravitational acceleration, but it does not depend upon the mass of the bob.
• Therefore the frequency of the simple pendulum will remain the same when the mass of the bob of a pendulum is increased.
• Hence, option 3 is correct.