A particle is released from height `H`. At certain height from the ground its kinetic energy is twice its gravitational potential energy. Find the height and speed of particle at that height.

Options

A. The height of the particle at that instant is `(H)/(2)`
B. The height of the particle at that instant is `(H)/(4)`
C. The speed of the particle at that instant is `sqrt((3gH)/(2))`
D. The speed of the particle at that instant is `(sqrt(3gH))/(2)`

Answer

B, C

Explanation

`U = 0`
`K = (1)/(2)mv^(2) = mgH_(2) = 3mgH_(1)`
`rArr H_(2) = 3H_(1)`……(1)
Also. `H_(1) + H_(2) = H` …..(2)
`rArr H_(1) = (H)/(4)` and `v = sqrt((3gH)/(2))`