1.

A particle is throws vertically upwards from the surface of earth and it reaches to a maximum height equal to the radius of earth. The radio of the velocity of projection to the escape velocity on the surface of earth isA. `(1)/(sqrt2)`B. `(1)/(2)`C. `(1)/(4)`D. `(1)/(2sqrt2)`

Answer» Correct Answer - A
Change in kinetic energy = change in potential energy
`:. (1)/(2) m nu^(2) = - (GMm)/(R + R) - (-(GMm)/(R))`
`t((GM)/(R)) = sqrt(2GM//R)/(sqrt(2))`
`= (nu_(e))/(sqrt(2))`
where, `nu_(e) =` escape velocity


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