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Second Law of Motion

A ball of mas...

Question

A ball of mass m is connected to a ball of mass M by means of a massless spring. The balls are pressed so that the spring is compressed. When released, the ball of mass m moves with an acceleration a. The magnitude acceleration of mass M will be equal to

A

$\frac{m a}{(M + m)}$

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B

$\frac{M a}{(M + m)}$

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C

$\frac{m a}{M}$

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D

$\frac{M a}{m}$

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Solution

The correct option is C
$\frac{m a}{M}$

When the balls are released, force experienced by mass m is F = ma.
This is the force exerted by mass M on mass m. From Newton's third law of motion, mass m will exert the same force F on mass M in opposite direction. Therefore, the acceleration of M is $a^{'} = \frac{F}{M} = \frac{m a}{M}$ and the correct choice is (c).

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