An object is kept at rest at a distance of 3R | vedclass

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(A) To ensure the object does not return to Earth,its total mechanical energy at infinity must be at least zero.Let $m$ be the mass of the object.The

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$\sqrt{\frac{GM}{2R}}$

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(A) To ensure the object does not return to Earth,its total mechanical energy at infinity must be at least zero.Let $m$ be the mass of the object.The distance of the object from the center of the Earth is $r = R + 3R = 4R$.The potential energy at this point is $U = -\frac{GMm}{4R}$.Let $v$ be the projection speed. The kinetic energy is $K = \frac{1}{2}mv^2$.By the law of conservation of energy:$K_i + U_i = K_f + U_f$$\frac{1}{2}mv^2 - \frac{GMm}{4R} = 0 + 0$$\frac{1}{2}mv^2 = \frac{GMm}{4R}$$v^2 = \frac{GM}{2R}$$v = \sqrt{\frac{GM}{2R}}$

An object is kept at rest at a distance of $3R$ above the earth's surface,where $R$ is the earth's radius. The minimum speed with which it must be projected so that it does not return to earth is (Assume $M =$ mass of earth,$G =$ Universal gravitational constant).

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