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A particle is released from a height h. ...

A particle is released from a height h. At a certain height, its kinetic energy is two times its potential energy. Height and speed of the particle at that instant are 

A

`h/3 sqrt((2gh)/(3))`

B

`h/3 2sqrt((gh)/(3))`

C

`(2h)/3 sqrt((2gh)/(3))`

D

`h/3 sqrt(2gh)`

Text Solution

Verified by Experts

The correct Answer is:
B
Total mechanical energy = mgh
As `(KE)/(PE) = 2/1`
`:. `KE = `2/3 mgh and PE = 1/3 mgh`
Height from the ground at that instant is `h. = h/3`
and speed of particle at that instant is
`v = sqrt(2g(h - h.)) = sqrt(2h((2h)/(3))) = 2sqrt((gh)/(3))`.
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Knowledge Check

  • A particle is released from a height S. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively

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