Home
Class 11
PHYSICS
When the displacement of a particle exec...

When the displacement of a particle executing SHM is one-fourth of its amplitude, what fraction of the total energy is the kinetic energy?

A

`(16)/(15)`

B

`(15)/(16)`

C

`(3)/(4)`

D

`(4)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
In SHM,
Kinetic energy of the particle, `K=(1)/(2)momega^(2)(A^(2)-x^(2))`
where m is the mass of particle, `omega` is its angular frequency, A is the amplitude of oscillation and x is its displacement.
At `x=(A)/(4),K=(1)/(2)momega^(2)[A^(2)-((A)/(4))^(2)]=(1)/(2)((15)/(16)momega^(2)A^(@))`
Energy of the particle, `E=(1)/(2)momega^(2)A^(2)`
`therefore=(K)/(E)=((1)/(2)((15)/(16)momega^(2)A^(2)))/((1)/(2)momega^(2)A^(2))=(15)/(16)`
Promotional Banner

Topper's Solved these Questions

  • OSCILLATIONS

    NCERT FINGERTIPS|Exercise Some Systems Executing Simple Harmonic Motion|29 Videos

  • OSCILLATIONS

    NCERT FINGERTIPS|Exercise Damped Simple Harmonic Motion|5 Videos

  • OSCILLATIONS

    NCERT FINGERTIPS|Exercise Force Law For Simple Harmonic Motion|2 Videos

  • MOTION IN A STRAIGHT LINE

    NCERT FINGERTIPS|Exercise Assertion And Reason|15 Videos

  • PHYSICAL WORLD

    NCERT FINGERTIPS|Exercise Assertion And Reason|10 Videos

Similar Questions

Explore conceptually related problems

When the displacement of a particle executing simple harmonic motion is half its amplitude, the ratio of its kinetic energy to potential energy is

When displacement of a particle executing SHM is half of the amplitude,its potential energy is 5 J. Find the total energy of the particle in SHM,if potential energy at mean position is zero.

A particle executes SHM with amplitude A and time period T. When the displacement from the equilibrium position is half the amplitude , what fractions of the total energy and kinetic and potential?

In a simple harmonic motion, when the displacement is one-half of the amplitude, what fraction of the total energy is kinetic?

In a simple harmonic motion, when the displacement is one-half the amplitude, what fraction of the total energy is kinetic ?

When displacement is one-third of the amplitude, what fraction of total energy is potential energy and what fraction is kinetic energy in simple harmonic motion ?

The total energy of a particle executing S.H.M. is proportional to