Question

Statement-1: Time period of simple pendulum is increased if density of material of pendulum is increased. Statement-2: Time period of simple pendulum is \( T = 2 \pi \sqrt{\frac{l}{g}} \).

• A. Statement I is true; Statement II is true
• B. Statement I is true; Statement II is false
• C. Statement I is false; Statement II is true
• D. Statement I is false; Statement II is false

Hint:

The time period of a simple pendulum depends on the length and gravitational acceleration, but not on the material density.

Answer 1

The Correct Option is C

To solve this question, we need to evaluate the truthfulness of two given statements about the time period of a simple pendulum.

Understanding Statement 1

Statement-1 claims: "Time period of simple pendulum is increased if density of material of pendulum is increased."

In the theory of simple pendulums, the time period T is not dependent on the mass or the density of the pendulum bob. The formula for the period of a simple pendulum is:

T = 2 \pi \sqrt{\frac{l}{g}}

From this formula, it is clear that the time period T depends only on l (the length of the pendulum) and g (the acceleration due to gravity), but not on the density of the material of the pendulum.

Therefore, Statement 1 is false.

Understanding Statement 2

Statement-2 claims: "Time period of simple pendulum is T = 2 \pi \sqrt{\frac{l}{g}}."

This is the standard formula for the time period of a simple pendulum, assuming small angle oscillations. Therefore, Statement 2 is true.

Conclusion

Based on the analysis above:

• Statement I is false because the time period does not depend on the density of the pendulum material.
• Statement II is true as it correctly describes the formula for the time period of a simple pendulum.

The correct answer is: Statement I is false; Statement II is true.