Simple Pendulum - Puzzles

Second's Pendulum Puzzles

1. What is the formula for the time period of a simple pendulum?

Hint: It depends on length and acceleration due to gravity.
T = 2π √(L/g)

2. What happens to the time period if the length of the pendulum is doubled?

Hint: Check the formula, T is proportional to √L.
The time period increases by a factor of √2.

3. What is the time period of a second’s pendulum?

Hint: It completes one oscillation in one second.
T = 2 seconds

4. What is the approximate length of a second’s pendulum on Earth?

Hint: Use the formula with g ≈ 9.8 m/s².
L ≈ 99 cm (or 1 metre)

5. What will happen to the time period of a pendulum if it is taken to the Moon?

Hint: The Moon’s gravity is about 1/6th of Earth's gravity.
The time period increases because gravity (g) is lower.

6. If the length of a pendulum is 4 times its original length, how does the time period change?

Hint: T is proportional to √L.
The time period doubles.

7. What is the unit of T²/L in SI units?

Hint: Consider T² = (2π)² (L/g).
The unit is s²/m.

8. If the acceleration due to gravity increases, what happens to the time period?

Hint: T is inversely proportional to √g.
The time period decreases.

9. Why do we take the mean of multiple time readings in the experiment?

Hint: It helps in reducing experimental errors.
To minimize random errors and improve accuracy.

10. Why is the pendulum set into oscillation with a small amplitude?

Hint: Large amplitude affects the simple harmonic motion.
To ensure the motion remains approximately simple harmonic.