A body is thrown from the surface of the earth with velocity u m/s. The maximum height in metre above the surface of the earth upto which it will reac is (where, R = radish of earth, g=acceleration due to gravity)

Options

A. `(u^(2)R)/(2gR-u^(2))`
B. `(2 u^(2)R)/(gR-u^(2))`
C. `(u^(2)R^(2))/(2g R^(2)-u^(2))`
D. `(u^(2)R)/(9R-u^(2))`

Answer

A

Explanation

`(GMm)/(R)+ 1/2m u ^(2) =0+ (Gm m)/((R+h))`
`(Gm )/((R +h))=(GM)/(R)-(u^(2))/(2)`
`(Gm)/((R+h))=(2G m - Ru ^(2))/(2R)`
`(R+h)/(GM ) =(2R)/(2GM -Ru^(2))`
`h=(2GMR)/(2GM Ru^(2))-R`
`=(2GMR- 2GMR+R^(2) u^(2))/(2GM -Ru^(2))`
`=(R^(2)u^(2))/(2GM -Ru ^(2))=(Ru^(2))/(2gR -u^(2))`