A particle is released from height `H`. At cartain 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. `(H)/(3),sqrt((2gH)/(3)`
B. `(H)/(3),2sqrt((gH)/(3)`
C. `(2H)/(3),sqrt((2gH)/(3)`
D. `(2H)/(3),sqrt(2gH)`

Explanation

[2]
`:' K+U=mgH &K=2U`
`:. 2U+U=MgH`
`rArrU=(mgH)/(3)rArrmgh=(mgH)/(3)rArrh=H//3`
`:. (1)/(2) mv^(2)=2U=(2mgH)/(3)rArr v=2 sqrt((gH)/(3))`