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: Understanding the Question:
The time period of a simple pendulum depends on the square root of its effective length.
Step 2: Key Formula or Approach:
Time period \( T = 2\pi \sqrt{\frac{L}{g}} \).
This implies \( T \propto \sqrt{L} \).
Step 3: Detailed Explanation:
Let \( T_1 = T \) and \( L_1 = L \).
New length \( L_2 = 3L \).
\[ \frac{T_2}{T_1} = \sqrt{\frac{L_2}{L_1}} = \sqrt{\frac{3L}{L}} = \sqrt{3} \]
\[ T_2 = \sqrt{3} T \]
Step 4: Final Answer:
The new time period is \( \sqrt{3} \) T.