UPSC Prelims 2001 · General Studies
Question 110: Science and Technology
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?
AnswerThe answer is (c).
Statements I, II and IV are correct. At the mean position the restoring (tangential) acceleration of the bob is zero and its speed is greatest. The bob passes through any given velocity twice in a cycle, and air resistance makes the amplitude shrink with time. Statement III is wrong: at the extreme position the velocity is zero but the acceleration is greatest.
- I. The restoring acceleration is zero at the mean position.
- II. A given velocity occurs twice in each cycle.
- III. At the extreme the velocity is zero but the acceleration is maximum.
- IV. Damping reduces the amplitude with time.
Why each option is right or wrong
- (a) IV is also correct.
- (b) III is wrong; acceleration is greatest at the extreme.
- (c) Right: I, II and IV.
- (d) III is wrong, and I is left out.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2001, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.