Two blocks of masses m₁ = 2 kg and m₂ = 5 kg are moving in the same direction along a frictionless surface with speeds $10 m s^{- 1} and 3 m s^{- 1}$ respectively. An ideal spring with $K = 1120 {Nm}^{- 1}$ is attached to the back side of m2. Find the maximum compression of the spring when the blocks collide.

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0.50 m

0.25 m

0.75 m

1 m

answer is B.

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Detailed Solution

Using conservation of linear momentum

$m_{1} \times 10 + m_{2} \times 3 = (m_{1} + m_{2}) V_{CM}$

$2 \times 10 + 5 \times 3 = 7 V_{cM}$

$V_{CM} = 5 m s^{- 1}$

At maximum compression of spring both particles will acquire common velocity $V_{CM} = 5 m s^{- 1}$

Energy conservation

$\frac{1}{2} 7 \times 5^{2} + \frac{1}{2} {kx}^{2}$ $\Rightarrow \frac{1}{2} k x^{2} = \frac{1}{2} \times 2 \times 10^{2} + \frac{1}{2} \times 5 \times 3^{2} - \frac{1}{2} \times 7 \times 5^{2}$

$\Rightarrow x = 0.25 m$

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