light, heat, thermodynamics, wave motion, sound, optics & oscillations - Category wise Question and Answer Practice Test with Solutions
light, heat, thermodynamics, wave motion, sound, optics & oscillations PRACTICE TEST [16 - EXERCISES]
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Question : 9
Consider the following statements for a simple harmonic motion:
- The magnitude of the velocity of the body is proportional to its displacement from the mean position.
- The magnitude of the acceleration of the body is proportional to its displacement from the mean position.
- The sum of the kinetic energy and potential energy of the body is always constant.
a) 3 only
b) 1 and 3
c) 2 and 3
d) 2 only
Answer »Answer: (c)
Let the displacement (y) of a particle executing SHM at an instant be given by.
y = a sin (ωt + φ)
velocity, v = ${dy}/{dt}$ = aω cos(ω + φ)
Hence, the magnitude of the velocity of a body is not proportional to its displacement from the mean position.
Acceleration, A = ${dv}/{dt}$ = –aω2 sin (ωt + φ) = - ω2y
Hence, |A| ∝ y
The total energy in SHM is given by
E = PE + KE = EP + EK = 1/2 mω2a2 = a constant
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