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  4. Assuming earth as a uniform sphere of radius R, if we project a body along the smooth diametrical chute from the centre of earth with a speed v such that it will just reach the earth’s surface then v is equal to:

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Q. Assuming earth as a uniform sphere of radius $R$, if we project a body along the smooth diametrical chute from the centre of earth with a speed $v$ such that it will just reach the earth’s surface then $v$ is equal to:

Gravitation

Solution:

image
$\left(KE + PE\right)_{1} = \left(KE +PE\right)_{2}$
$ \frac{1}{2}mv^{2} - \frac{3}{2} \frac{GMm}{R} = -\frac{GMm}{R} $
$ v = \sqrt{\frac{GM}{R}} = \sqrt{\frac{gR^{2}}{R}}$
$ = \sqrt{gR} $