Question

A simple pendulum oscillates with a small amplitude. Its length is doubled and its mass is halved. What happens to the frequency of its motion?

1) It becomes 1/√2 as large.
2) It doubles.
3) The frequency is unchanged.
4) It becomes √2 as large.
5) It becomes half as large.

Answer 1

When the length of a simple pendulum is doubled and its mass is halved, the frequency of its motion remains unchanged.

Step-by-step explanation:

In a simple pendulum, the frequency of its motion is given by the formula:

f = (1/2π) × √(g/L)

where f is the frequency, g is the acceleration due to gravity, and L is the length of the pendulum.

1. If the length of the pendulum is doubled, the new frequency becomes:
2. f' = (1/2π) × √(g/2L)
3. If the mass of the pendulum is halved, the new frequency becomes:
4. f'' = (1/2π) × √(2g/L)

Comparing f' and f'', we can see that the frequency remains unchanged. Therefore, the correct answer is 3) The frequency is unchanged.