A stationary object is released from a point P a distance 3 R from the centre of the moon which has radius R and mass M . Which one of the following expressions gives the speed of the object on hittin

Question

A stationary object is released from a point P a distance 3 R from the centre of the moon which has radius R and mass M . Which one of the following expressions gives the speed of the object on hitting the moon?

TestHub · Accepted Answer

According to the law of conservation of energy,

$- \frac{G m M}{3 R} + \frac{m v_{0}^{2}}{2} = - \frac{G m M}{R} + \frac{m v_{1}^{2}}{2}$

Where $m$ is the mass of the object, $v_{0}$ and $v_{1}$ are the initial and final velocities of object, respectively.

The object is stationary i.e., $v_{0} = 0 .$

$\Rightarrow - \frac{G M}{3 R} = - \frac{G M}{R} + \frac{v_{1}^{2}}{2}$

$\Rightarrow \frac{v_{1}^{2}}{2} = \frac{2 G M}{3 R}$

$\Rightarrow v_{1} = 2 \sqrt{\frac{G M}{3 R}} = {(\frac{4 G M}{3 R})}^{\frac{1}{2}}$

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