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.You need to login to perform this action.
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