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Two blocks of masses $m a n d 2 m$ are connected by a compressed spring with a string as shown in figure. The spring has an initial compression of $x = 1 m$ . The force constant $k = 6 N / m$ . Whole system is moving towards right with speed $1 m / s$ . Now if the spring is cut, then (Take $m = 1 k g$ and no friction anywhere)

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when $m$ is having maximum speed, the energy stored in the spring will be $6 J$ .

when $m$ is having maximum speed, the energy stored in the spring will be $3 J$ .

the minimum speed attained by $2 m$ is zero.

The maximum speed attained by $m i s 3 m / s$ .

answer is B, D.

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Detailed Solution

When the spring attains its naturl length,velocity of m is $v_{1}$ and that of 2m is $v_{2} .$

$\frac{1}{2} k {(1)}^{2} = \frac{1}{2} \times 1 \times v_{1}^{2} + \frac{1}{2} \times 2 \times v_{2}^{2}$

and $1 \times v_{1} = 2 v_{2}$

$∴ v_{2} = 1 m / s (l e f t) a n d v_{1} = 2 m / s (r i g h t)$

Therefore maximum velocity of $m$ becomes $2 + 1 = 3 m / s$ and minimum velocity of $2 m$ becomes $= 1 - 1 = 0$

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