Q75 / 90 · JEE Main 2021 (31 Aug Shift 2) · Physics

For a body executing S.H.M. :
(a) Potential energy is always equal to its K.E.
(b) Average potential and kinetic energy over any given time interval are always equal.
(c) Sum of the kinetic and potential energy at any point of time is constant.
(d) Average K.E. in one time period is equal to average potential energy in one time period.
Choose the most appropriate option from the options given below :

  • Correct answer
    A
    (c) and (d)
  • B
    only (c)
  • C
    only (b)
  • D
    (b) and (c)

Solution

The formula of kinetic energy in S.H.M. is, K.E.=12mω2A2-x22, where A is the amplitude of the S.H.M. the formula of potential energy is, P.E.=12mω2x2, so the net energy is defined as, T.E.=P.E.+K.E.=12mω2A2 so the total energy is always constant. Since, energy changes from potential to kinetic and vice-versa the average K.E. in one time period is equal to the average P.E. in one time period.

Hence, the correct answer is option: 'A'.

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