A particle is realesed from a height `H` from ground. At certain height its kinetic energy is three times its gravitational potential energy with respect to ground. Then choose the correct option(s). (Given `'g'` is acceleration due to gravity is constant).

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))`