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 point Q above the earth to tis highest point and back to the same Q. If the distance between the points 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))`
`rArrT_(p)^(2)=(8(h+H))/(g)& T_(Q)^(2)=(8h)/(g)rArrT_(P)^(2)=T_(Q)^(2)+(8H)/(g)`
`rArrg=(8H)/(T_(P)^(2)-T_(Q)^(2))`