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A 30 kg shell in free space explodes into three identical fragments. After the explosion, the fragments rush apart. Forces of mutual interaction between the fragments are long range attractive conservative forces. Immediately after the explosion, velocities of the fragments relative to an inertial frame are $(3 \hat{i} + 2 \hat{j}) m / s, - 2 \hat{i} m / s$ and $(5 \hat{i} - 5 \hat{j}) m / s$ . If entire energy released in the explosion is converted into kinetic energy of fragments then:

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Energy released in explosion is 335 J

Energy released in explosion is 260 J

After sufficiently long time, when the forces of mutual interaction ceases to act, total kinetic energy of fragments become minimum.

After sufficiently long time, total kinetic energy of all fragments is 75 J

answer is B, C, D.

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Detailed Solution

Energy release $Q = \tilde{K} = {\tilde{K}}_{1} + {\tilde{K}}_{2} + {\tilde{K}}_{3}$

$= \frac{1}{2} \times 10 {{\tilde{V}}_{1}^{2} + {\tilde{V}}_{2}^{2} + {\tilde{V}}_{3}^{2}} = \frac{1}{2} \times 10 \times {{(1 i + 3 j)}^{2} + {(- 4 i + j)}^{2} + {(3 \hat{i} + 4 j)}^{2}}$

$= 5 {10 + 17 + 25} = 260 J$ ${\bar{V}}_{c} = \frac{{\bar{V}}_{1} + {\bar{V}}_{2} + {\bar{V}}_{3}}{3}$ $= 2 \hat{i} - \hat{j}$

$∴ K_{\min} = \frac{1}{2} M V_{c}^{2} = \frac{1}{2} \times 30 \times 5 = 75 J$

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