Question

If the length of a pendulum is made 9 times and mass of bob is made 4 times, then the value of time period becomes

• A. 3T
• B. \(\frac{3}{2}T\)
• C. 4T
• D. 2T

Hint:

Time period of simple pendulum depends only on length and g, not on mass or amplitude (for small angles).

Answer 1

The Correct Option is A

The time period of a simple pendulum is given by the formula:

\(T = 2\pi \sqrt{\frac{L}{g}}\)

Where:

• \(T\) is the time period.
• \(L\) is the length of the pendulum.
• \(g\) is the acceleration due to gravity.

Importantly, the time period \(T\) is independent of the mass of the bob.

Now, according to the question, if the length of the pendulum is made 9 times its original length, the new length \(L_{\text{new}}\) will be:

\(L_{\text{new}} = 9L\)

The mass of the bob does not affect the time period, so it remains irrelevant in this situation.

Therefore, substituting the new length \(L_{\text{new}}\) in the time period formula, we get:

\(T_{\text{new}} = 2\pi \sqrt{\frac{L_{\text{new}}}{g}} = 2\pi \sqrt{\frac{9L}{g}} = 2\pi \times 3 \sqrt{\frac{L}{g}} = 3(2\pi \sqrt{\frac{L}{g}})\)

Thus, \(T_{\text{new}} = 3T\).

So, the correct answer to the question is 3T.

Let's examine the options:

• \(3T\) - This is the correct answer as calculated.
• \(\frac{3}{2}T\) - Incorrect as it doesn't match our calculation.
• \(4T\) - Incorrect, since the time period is proportional to the square root of the length.
• \(2T\) - Incorrect for similar reasons to above.

In conclusion, when the length is increased by a factor of 9, the time period becomes 3T, irrespective of any change in the mass of the bob.