Home
Class 11
PHYSICS
Assertion : Average kinetic energy in on...

Assertion : Average kinetic energy in one oscillation during SHM of a body is `(1)/(4)momega^(2)A^(2)`.
Reason : Maximum kinetic energy is `(1)/(2)momega^(2)A^(2)`.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is true but Reason is false.

D

If Assertion is false but Reason is true.

Text Solution

Verified by Experts

The correct Answer is:
B
(b) If `v=omegaA " sin"omegat`
Then, `v_("max")=omegaA`
`therefore K_("max")=(1)/(2)mv_("max")^(2)=(1)/(2)momega^(2)A^(2)`
Further , `gtAlt = lt (1)/(2)momega^(2)A^(2)"sin"^(2)omegat gt `
`(1)/(2)momega^(2)A^(2) lt "sin"^(2)omegatlt `
But `lt "sin"^(2) gt =(1)/(2)` in one oscillation
`therefore lt K gt =(1)/(4)momega^(2)A^(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The average kinetic energy associated with one mole of a gas is

What is average kinetic energy of 1 mole of SO_(2) at 300 K?

Find the average kinetic energy of a simple harmonic oscillator if its total energy is 10 joule and minimum potential energy is 2 joule.

The average kinetic energy of a simple harmonic oscillator is 2 joule and its total energy is 5 joule. Its minimum potential energy is

At which position the kinetic energy of a harmonic oscillator is maximum or minimum ?

At which position the kinetic energy of a harmonic oscillator is maximum or minimum ?

The average value of kinetic energy in an SHM is (Symbols have usual meanings)

A particle executing SHM possesses two types of energy. Potential energy is on account of displacement of particle from the mean positoin, anad kinetic energy is ono account of velocity of the particle. At any time t P.E. =U=(1)/(2)momega^(2)y^(2)=(1)/(2)momega^(2)a^(2)sin^(2)omegat, and K.E..=K=(1)/(2)momega^(2)(a^(2)-y^(2))=(1)/(2)momega^(2)a^(2)cos^(2)omegat T.E. =E=U+K=(1)/(2)momega^(2)a^(2)= constant Read the above passage and answer the following questions: (i) At what distance from the mean position will K.E. of a particle be twice its P.E.? (ii) What are the implications of this study in day life?