Question

The length of the simple pendulum is made 3 times the original length. If \( T \) is its original time period, then the new time period will be

• A. \( 3T \)
• B. \( \sqrt{3} T \)
• C. \( 2T \)
• D. \( \sqrt{3} T \)

Hint:

For a simple pendulum, the time period depends on the square root of the length of the pendulum. If the length is tripled, the time period increases by a factor of \( \sqrt{3} \).

Answer 1

The Correct Option is B

Step 1: Time period of a simple pendulum.
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,
- \( g \) is the acceleration due to gravity.

Step 2: New length of the pendulum.
When the length of the pendulum is increased to 3 times its original length, the new length \( L_{\text{new}} \) is:
\[ L_{\text{new}} = 3L. \]

Step 3: Time period with the new length.
The new time period \( T_{\text{new}} \) for the pendulum with length \( L_{\text{new}} \) is:
\[ T_{\text{new}} = 2\pi \sqrt{\frac{L_{\text{new}}}{g}} = 2\pi \sqrt{\frac{3L}{g}} = \sqrt{3} \cdot 2\pi \sqrt{\frac{L}{g}} = \sqrt{3} \cdot T. \]
Final Answer:
Thus, the new time period is:
\[ \boxed{\sqrt{3} T}. \]