Question

Time period of a simple pendulum will be doubled if we

• A. increase the length two times.
• B. decrease the length two times.
• C. decrease the length four times.
• D. increase the length four times.

Hint:

The time period of a pendulum is directly proportional to the square root of its length.

Answer 1

The Correct Option is D

Step 1: Using the formula for the time period.
The time period \( T \) of a simple pendulum is given by the formula: \[ T = 2\pi \sqrt{\frac{L}{g}} \] where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.
Step 2: Effect of changing the length.
If the length is increased by a factor of 4, the time period increases by a factor of \( \sqrt{4} = 2 \). Hence, the time period will be doubled.
Step 3: Conclusion.
The correct answer is (D), increase the length four times.