A) 1 : 1
B) 1 : 2
C) 2 : 1
D) 1 : 4
Correct Answer: A
Solution :
Given, \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{1}{4}\] and \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{4}{1}\] As \[K=\frac{{{p}^{2}}}{2m}\] So, \[\frac{p_{1}^{2}}{2{{m}_{1}}}=4\left( \frac{p_{2}^{2}}{2{{m}_{2}}} \right)\] \[\Rightarrow \] \[\frac{p_{1}^{2}}{P_{2}^{2}}=4\left( \frac{{{m}_{1}}}{{{m}_{2}}} \right)=4\left( \frac{1}{4} \right)\] \[\Rightarrow \] \[\frac{{{p}_{1}}}{{{p}_{2}}}=1\] Or \[{{p}_{1}}:{{p}_{2}}=1:1\]
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