• question_answer A body is thrown vertically upwards from the surface of earth in such a way that it reaches upto a height equal to $10{{R}_{e}}$. The velocity imparted to the body will be A)  $10.6\,km/s$               B)  $0.106\,km/s$C)  $1.06\,km/s$               D)  zero

Work done in going from a distance ${{r}_{1}}$ to a distance ${{r}_{2}}$away from centre of the earth, by a body of mass m, is, $W=GMm(1/{{r}_{1}}-1/{{r}_{2}}),$ For our case we should have $1/2m{{v}^{2}}=GMn[(1/{{R}_{e}})-(1/10{{R}_{e}})]$ $=(GMm/{{R}_{e}})\times (9/10)$ $v=\sqrt{{}}[(2GM/{{R}_{e}})\times (9/10)]=\sqrt{{}}(9/10)\times$escape velocity $\sqrt{{}}(9/10)\times 11.1km/s=10.6km/s$