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(B) By applying the law of conservation of mechanical energy between the Earth's surface and the maximum height reached by the body:Initial Mechanical

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$R$

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(B) By applying the law of conservation of mechanical energy between the Earth's surface and the maximum height reached by the body:Initial Mechanical Energy $(E_i)$ = Final Mechanical Energy $(E_f)$$P.E._i + K.E._i = P.E._f + K.E._f$$-\frac{G M m}{R} + \frac{1}{2} m \left(\sqrt{\frac{G M}{R}}\right)^2 = -\frac{G M m}{r} + 0$$-\frac{G M m}{R} + \frac{G M m}{2 R} = -\frac{G M m}{r}$$-\frac{G M m}{2 R} = -\frac{G M m}{r}$$r = 2 R$Since $r = R + h$,where $h$ is the height above the surface:$R + h = 2 R$$h = R$

$A$ body is projected vertically upwards with a speed of $\sqrt{\frac{G M}{R}}$ ($M$ is the mass and $R$ is the radius of the Earth). The body will attain a maximum height of .......

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