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 the particle to travel from another point Q above the earth to its highest point and back to the same point Q. if the distance between the point P and Q is H, find the expression for acceleration due to gravity in terms of `T_(P).T_(Q)` and H.

Explanation

Time taken from point P to point P `" "T_P= 2sqrt((2(h+H))/(g))`
Time taken from point Q to point Q `" "T_Q = 2sqrt((2h)/(g))`
`rArr T_P^(2)= (8(h+H))/(g) & T_(Q)^(2)= (8h)/(g) rArr T_P^(2)= T_(Q)^(2) + (8H)/(g)`
`rArr g = (8H)/(T_(P)^(2)-T-(Q)^(2))`