UPSC Prelims 2001 Q110: Science & Technology – Physics
Consider the following statements: A simple pendulum is set into oscillation. Then
I. The acceleration is zero when the bob passes through the mean position.
II. In each cycle the bob attains a given velocity twice.
III. Both acceleration and velocity of the bob are zero when it reaches its extreme position during
its oscillation.
IV. The amplitude of oscillation of the simple pendulum decreases with time.
Which of these statements are correct?
- (a) I and II
- (b) III and IV
- (c) I, II and IV
- (d) II, III and IV
Answer: (c) I, II and IV
Explanation
Statements about a simple pendulum in oscillation
| Statement | Verdict |
|---|---|
| I. Acceleration is zero when the bob passes the mean position | Correct — the restoring (tangential) acceleration is zero there |
| II. In each cycle the bob attains a given velocity twice | Correct — once each way past the same point |
| III. Both acceleration and velocity are zero at the extreme position | Wrong — velocity is zero but acceleration is maximum |
| IV. Amplitude decreases with time | Correct — air resistance and friction damp the motion |
At the mean position speed is greatest and the restoring acceleration is zero. At the extreme position the bob stops for an instant but its acceleration is greatest. A real pendulum slowly loses energy, so its amplitude falls. So I, II and IV are correct.
Answer: (c) I, II and IV.
Why each option is right or wrong
- (a) Incorrect. Statement IV, the damping of amplitude, is also correct.
- (b) Incorrect. Statement III is wrong; acceleration is greatest at the extremes.
- (c) CORRECT. I, II and IV are correct; III is wrong.
- (d) Incorrect. Statement III is wrong.
Key point
In SHM: velocity maximum and acceleration zero at the mean; velocity zero and acceleration maximum at the extremes.
Remember
Pendulum: mean — max speed, zero acceleration; extreme — zero speed, max acceleration.
Common mistakes
- Thinking acceleration is zero wherever velocity is zero.
- Forgetting real pendulums are damped.
- Missing that each speed is reached twice per cycle.
Exam tip
Velocity and acceleration in SHM are out of step: one is largest where the other is zero.
Sources
- NCERT Class XI — Physics Part II, chapter 'Oscillations'
- NCERT Class VII — Science, chapter 'Motion and Time' (simple pendulum)