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. 3 T
• B. \(\sqrt{3}\text{ }\mathrm{T}\)
• C. \(\frac{\mathrm{T}}{\sqrt{3}}\)
• D. \(\frac{\mathrm{T}}{3}\)

Hint:

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

Answer 1

The Correct Option is B

Step 1: Write both periods
$T=2\pi\sqrt{L/g}$ and $T'=2\pi\sqrt{3L/g}$.

Step 2: Divide
$T'=\sqrt{3}\times2\pi\sqrt{L/g}$.

Step 3: Result
$T'=\sqrt{3}\,T$, so option (B) is correct.

Final Answer:
Option (B) is correct. \[ \boxed{\text{(B) }\sqrt{3}\text{ }\mathrm{T}} \]