A) \[{{M}_{B}}:{{M}_{A}}\]
B) \[{{M}_{A}}:{{M}_{B}}\]
C) \[\sqrt{{{M}_{A}}}:\sqrt{{{M}_{B}}}\]
D) \[{{M}_{A}}^{2}:{{M}_{B}}^{2}\]
Correct Answer: C
Solution :
We know,\[K.E.=\frac{1}{2}m{{v}^{2}}=\frac{{{p}^{2}}}{2m}\] Since, \[K.E.\] is same for both bodies, therefore \[K.E.=\frac{{{P}_{A}}^{2}}{2{{M}_{A}}}=\frac{{{P}_{B}}^{2}}{2{{M}_{B}}}\] \[\Rightarrow \] \[\frac{{{P}_{A}}^{2}}{{{P}_{B}}^{2}}=\frac{2{{M}_{A}}}{2{{M}_{B}}}=\frac{{{M}_{A}}}{{{M}_{B}}}\] \[\Rightarrow \] \[\frac{{{P}_{A}}}{{{P}_{B}}}=\frac{\sqrt{{{M}_{A}}}}{\sqrt{{{M}_{B}}}}\] \[\Rightarrow \] \[\left| {{P}_{A}} \right|:\left| {{P}_{B}} \right|=\sqrt{{{\mathbf{M}}_{\mathbf{A}}}}\mathbf{:}\sqrt{{{\mathbf{M}}_{\mathbf{B}}}}\]
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