Two spheres are placed into free fall from rest. Sphere B has a mass three times larger than sphere A. Which statement(s) correctly explains the situation?
I. Sphere B falls faster.
II. Sphere B has more momentum when the two reach the ground.
III. Both spheres reach the ground with the same kinetic energy

I only

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II only

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I and III only

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II and II only

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I, II, and III

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Solution

The correct option is A II only
The acceleration of both the spheres is same and equal to $g$ independent of the mass of the sphere.
Hence the speed of both is same after falling through same height $h$ and equal to $\sqrt{2 g h}$ .
Thus the momentum $m v$ of sphere B is thrice that of A.
And also the kinetic energy $\frac{1}{2} m v^{2}$ of sphere B is thrice that of sphere A.
Hence correct answer is option B.

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