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?

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?, 2 G M 3 R 1 2, 4 G M 3 R 1 2, 2 G M R 1 2, G M R 1 2

MARKS App · Accepted Answer

According to the law of conservation of energy, - G m M 3 R + m v 0 2 2 = - G m M R + 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 . ⇒ - G M 3 R = - G M R + v 1 2 2 ⇒ v 1 2 2 = 2 G M 3 R ⇒ v 1 = 2 G M 3 R = 4 G M 3 R 1 2

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