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Simple Harmonic Motion question

2021 · 26 Feb · Shift 2 · Q66
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  5. /2021 · 26 Feb · Shift 2 · Q66

Simple Harmonic Motion question

2021 · 26 Feb · Shift 2 · Q66

JEE MainPhysicsSimple Harmonic MotionMCQ+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 :
  1. A
    Both Statement I and Statement II are false
  2. B
    Statement I is false but Statement II is true
  3. C
    Both Statement I and Statement II are true
  4. D
    Statement I is true but Statement II is false
View written solutionFree

Correct answer: B

  1. Meaning of a second's pendulum

A second's pendulum is defined as a pendulum whose time period is: T=2 sT = 2\text{ s}T=2 s So, Statement I says it has time period 1 s1\text{ s}1 s, which is incorrect.

Hence, Statement I is false.

  1. Time taken to move from one extreme position to the other

For a pendulum executing SHM:

  • Time for one complete oscillation =T= T=T
  • Time to go from one extreme to the mean position =T/4= T/4=T/4
  • Time to go from one extreme to the other extreme =T/2= T/2=T/2

For a second's pendulum, T=2 sT=2\text{ s}T=2 s. Therefore, time from one extreme to the other is: T2=22=1 s\frac{T}{2} = \frac{2}{2} = 1\text{ s}2T​=22​=1 s So, Statement II is true.

  1. Conclusion
  • Statement I: False
  • Statement II: True

Therefore, the correct option is: B\boxed{\text{B}}B​

  1. Comparison with stored answer

Stored correct answer: B

My derived answer matches the stored answer.

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