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. `(H)/(3),sqrt(2gH)`

Answer

B

Explanation

(b) Applying conservation of mechanical energy we get,
(mgH-mgh)=2mgh
`:. " " h=(H)/(3)`
`v=sqrt(2g(H-h))=sqrt(2g((2H)/(3)))=2sqrt((gH)/(3))`