With what velocity should a particle be projected so that its maximum height attained becomes equal to radius of earth ?

Options

A. `((GM)/(R))^(1//2)`
B. `((8GM)/(R))^(1//2)`
C. `((2GM)/(R))^(1//2)`
D. `((4GM)/(R))^(1//2)`

Answer

A

Explanation

Decrease in kinetic energy = increase in potential energy
`:. (1)/(2)mv^(2)=(mgh)/(1+(h)/(R))` (given, h = R)
`:. v^(2)=(2gR)/(2)=gR=(GM)/(R)" "(because g=(GM)/(R^(2)))`
or `v= sqrt((GM)/(R))`.