The velocity with which a projectile must be | vedclass

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(B) The escape velocity is the minimum initial velocity required for an object to escape the gravitational field of a planet and never return. For an

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Mass of the projectile

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(B) The escape velocity is the minimum initial velocity required for an object to escape the gravitational field of a planet and never return. For an object of mass $m$ to escape from the surface of the Earth (mass $M_e$,radius $R_e$),its initial kinetic energy must be equal to the magnitude of its gravitational potential energy. $\frac{1}{2} m v_e^2 = \frac{G M_e m}{R_e}$ Solving for $v_e$,we get: $v_e = \sqrt{\frac{2 G M_e}{R_e}}$ From this formula,it is clear that the escape velocity $v_e$ depends only on the gravitational constant $G$,the mass of the Earth $M_e$,and the radius of the Earth $R_e$. It is independent of the mass of the projectile $m$. Therefore,the correct option is $B$.

The velocity with which a projectile must be fired so that it escapes Earth's gravitation does not depend on

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