A particle is thrown vertically upwards from the surface of the earth. Let `T_(P)` be the time taken by the particle to travel from a point P above the earth to its highest point and back to the point P. Similarly, let `T_(Q)` be the time taken by the particle to travel from another point Q above the earth to its highest point and back to the same in terms of `T_(P), T_(Q)` and H, is :-

Explanation

Time taken from point P to poinr P
`T_(P)=T_(PR)+T_(RP)`
Here, `T_(PR)=T_(RP)` then `T_(PP)=2T_(PR)`
Using second equation of motion.
`(H+h)=(1)/(2)gT_(PR)^(2) rArr T_(PR) = sqrt(2((H+h))/(g))`

Then similarly, time taken from point Q to point Q
`T_(Q)=2sqrt((2h)/(g)) rArr T_(P)^(2)=(8(h+H))/(g)` and `T_(Q)^(2)=(8h)/(g)`
`rArr T_(P)^(2)=T_(Q)^(2)+(8H)/(g) rArr g=(8H)/(T_(P)^(2)-T_(Q)^(2))`