A) 1 : 2
B) 1 : 1
C) 4 : 1
D) 1 : 4
Correct Answer: D
Solution :
The kinetic energy of a body of mass m moving with velocity v is \[K=\frac{1}{2}\,m{{v}^{2}}\] Its linear momentum \[p=mv\] \[\therefore \] \[K=\frac{1}{2m}\,{{(mv)}^{2}}\] \[orK=\frac{{{p}^{2}}}{2m}\] \[\therefore \frac{{{K}_{1}}}{{{K}_{2}}}=\frac{p_{1}^{2}}{2{{m}_{1}}}\times \frac{2{{m}_{2}}}{p_{2}^{2}}\] but \[{{p}_{1}}={{p}_{2}}\] (given) \[So,\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}\] \[or\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{{{K}_{2}}}{{{K}_{1}}}=\frac{1}{4}\] Thus, \[{{m}_{1}}:{{m}_{2}}=1:4\]
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