A) 1
B) \[{{m}_{1}}{{v}_{2}}/{{m}_{2}}{{v}_{1}}\]
C) \[{{m}_{2}}/{{m}_{1}}\]
D) \[{{m}_{1}}/{{m}_{2}}\]
Correct Answer: C
Solution :
Key Idea: For a exploding body, linear momentum is conserved. From conservation of linear momentum, \[{{P}_{initial}}={{P}_{final}}\] \[0={{m}_{1}}{{v}_{1}}-{{m}_{2}}{{v}_{2}}\] Or \[{{m}_{1}}{{v}_{1}}={{m}_{2}}{{v}_{2}}\] Or \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}\] Thus, ratio of kinetic energies, \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{\frac{1}{2}{{m}_{1}}v_{1}^{2}}{\frac{1}{2}{{m}_{2}}v_{2}^{2}}=\frac{{{m}_{1}}}{{{m}_{2}}}\times {{\left( \frac{{{m}_{2}}}{{{m}_{1}}} \right)}^{2}}\] \[=\frac{{{m}_{2}}}{{{m}_{1}}}\] Note: In a collision of two bodies whether it is perfectly elastic or inelastic, linear momentum is always conserved but kinetic energy need not to be conserved.
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