Two balls of mass $1 k g$ and $2 k g$ respectively are connected to the two ends of the spring. The two balls are pressed together and placed on a smooth table. When released, the lighter ball moves with an acceleration of $2 {m s}^{- 1}$ . The acceleration of the heavier ball will be:

0.2 {m s}^{- 2}

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1 {m s}^{- 2}

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2 {m s}^{- 2}

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4 {m s}^{- 2}

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Solution

The correct option is C $1 {m s}^{- 2}$
Let $a^{'}$ be the acceleration of $2 k g$ mass.
for block of mass $1 k g$ : $a = - k x . . . (1)$
for block of mass $2 k g$ : $2 a^{'} = - k x . . (2)$
$(2) / (1), \frac{2 a^{'}}{a} = 1 \Rightarrow a^{'} = \frac{a}{2} = \frac{2}{2} = 1 m / s^{2}$

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