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For a particle executing S.H.M. which of...

For a particle executing S.H.M. which of the following statements holds good `:`

A

The mechanical energy of particle remains constant

B

The restoring force is always directed towards a fixed point

C

The velocity is minimum at the equilibrium position

D

The restoring force is maximum at the extreme position

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
In S.H.M., Restoring force `F=-ky,` Here, `-ve` sign shows that it is directed towards mean position. Restoring force is maximum when `y=1=` amplitude of S.H.M. It means the particle is at the extreme position. The total energy of the particle, `E=(1)/(2)momega^(2)a^(2)=a` constant.
The velocity is maximum at the mean position.
Choices `(a,b,d)` are correct.
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Knowledge Check

  • For a particle executing SHM, which of the following statements does not hold good ?

    A
    the total energy of the particle always remains the same
    B
    the restoring force is always directed towards a fixed point
    C
    the restoring force is maximum at the extreme positions
    D
    the velocity of the particle is minimum at the centre of motion of the particle

  • If a= -omega^(2) x represents the acceleration of a particle executing S.H.M.which of the following statement(s) is // are correct ?

    A
    a' is maximum at the extreme position
    B
    Timeperiod is `T = 2pi sqrt( omega )`
    C
    At `x=0`, the potential energy is maximum
    D
    At x=0 , the K.E. is maximum

  • If x, v, a, K.E. and P.E. represent displacement, velocity, acceleration, kinetic energy and potential energy at any instant respectively for a particle executing S.H.M., then which of the following statements is INCORRECT?

    A
    v and x may have same direction
    B
    v and a may have same direction
    C
    a and x may have same direction
    D
    K.E and P.E may have same value.

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