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

Step 1: Analyze Statement 1.
The time period of a simple pendulum depends only on the length \( l \) and acceleration due to gravity \( g \), not on the density of the material of the pendulum. Therefore, Statement 1 is false. Step 2: Analyze Statement 2.
The time period of a simple pendulum is indeed given by the formula: \[ T = 2 \pi \sqrt{\frac{l}{g}}, \] where \( l \) is the length and \( g \) is the acceleration due to gravity. Thus, Statement 2 is true. Step 3: Conclusion.
Therefore, Statement I is false and Statement II is true. Final Answer: \[ \boxed{\text{Statement I is false; Statement II is true.}} \]