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, |
| \[{{P}_{inititial}}={{P}_{final}}\] |
| \[0={{m}_{1}}{{v}_{1}}-{{m}_{2}}{{v}_{2}}\] |
| or \[{{m}_{1}}{{v}_{1}}={{m}_{2}}{{v}_{2}}\] |
| or \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}\] (i) |
| Thus, ratio of kinetic energies, |
| \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{\frac{1}{2}{{m}_{1}}v_{1}^{2}}{\frac{1}{2}{{m}_{2}}v_{2}^{2}}=\frac{{{m}_{1}}}{{{m}_{2}}}\times {{\left( \frac{{{m}_{2}}}{{{m}_{1}}} \right)}^{2}}\]\[=\frac{{{m}_{2}}}{{{m}_{1}}}\] |
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