JEE Main 2021 · 26 February · evening · Single correct · +4 / −1
Given below are two statements :
Statement I : A second's pendulum has a time period of 1 second.
Statement II : It takes precisely one second to move between the two extreme positions.
In the light of the above statements, choose the correct answer from the options given below :
- (a) Both Statement I and Statement II are false
- (b) Statement I is false but Statement II is true
- (c) Both Statement I and Statement II are true
- (d) Statement I is true but Statement II is false
Answer and solution
Answer (b) Statement I is false but Statement II is true
Solution
Physics sir · 4 steps
A seconds pendulum is named for each swing, not the full trip: one swing is 1 s, so T = 2 s.
- What the name means. A seconds pendulum is defined as one that takes 1 s to swing from one extreme to the other. A full oscillation is out and back, which is two such swings.
T = 2 × 1 s = 2 s
- Check Statement I. The time period is the time for one complete oscillation, which is 2 s, not 1 s. So Statement I is false.
- Check Statement II. Going from one extreme to the other is half an oscillation, so it takes T/2 = 1 s. So Statement II is true.
- So. Statement I is false and Statement II is true, which is option (b).
The idea to keep. A seconds pendulum ticks once per second, one tick for each swing. Its period, out and back, is 2 s, and from T = 2π√(L/g) its length on Earth is close to 1 m.
Answer from the NTA final answer key. Solution by PrepWiser.