Chapter 25, Problem 31A

Does the period of a pendulum depend of the mass of the bob? On the length of the string?

To determine

To identify: Whether the period of a pendulum depend on the mass of the bob as well as on the length of the string.

Answer to Problem 31A

No, the period of a pendulum does not depend on the mass of the bob. But it depends on the length of string.

Explanation of Solution

Introduction:

The time period T of a pendulum is defined as thetime taken to complete one back and forth motion from rest. Mathematically, it can be expressed as,

  $T=2\pi \sqrt{\frac{l}{g}}$

Here,

g denotes the acceleration due to gravity

l denotes the length of the string of the pendulum

From the equation, it can be inferred that the period of the pendulum is independent of bob’s.

Now, it can also be seen that the period is directly proportional to square root of the length of the string,

  $T\propto \sqrt{l}$

Conclusion:

Therefore, the period of the pendulum does not depend on the mass of bob but it depends upon the length of string.