Chapter 11, Problem 1OQ

To determine

To Choose: The correct option.

Answer to Problem 1OQ

Solution:

Option C. The frequency of the pendulum would remain the same.

Explanation of Solution

Given:

Mass of the pendulum, $m$

Length of the string, $l$

The angle of the string from the vertical, ${\theta }_1=5°$

Frequency of the pendulum, $f$

The new angle of the pendulum, ${\theta }_2=10°$

Formula used:

The frequency of the pendulum is given by the formula

  $f=\frac{1}{2\pi }\sqrt{\frac{g}{l}}$

Here,

  $g$ is the acceleration due to gravity.

  $l$ is the length of the string.

Since it is clear from the formula of frequency that it does not depend upon the angle at which it tilts, instead it depends only on the length of the string, Therefore, one can say that in each case, the frequency of the pendulum would remain the same.

Conclusion:

The frequency of the simple pendulum depends only on the length of the string.