A simple pendulum is made of a hollow sphere containing mercury suspended by means of a wire. If a little mercury is drained off, the period of the pendulum will:
Correct answer: B. increase:
- A. remain the same:
- B. increase:
- C. decrease
- D. B, C
Explanation
When only a little mercury is drained from the initially full sphere, the centre of gravity of the remaining mercury shifts downward, so the effective length L of the pendulum increases. Since T = 2π√(L/g), the period increases. (Only as the sphere nears empty does the centre of gravity rise again and the period fall; for a small amount drained the period increases.)
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About Simple Harmonic Motion
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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