A) double
B) tripled
C) increases by \[\sqrt{2}\]times
D) remains unchanged.
Correct Answer: C
Solution :
Given, \[K.{{E}_{1}}=K.E.\]and \[K.{{E}_{2}}=2K.E{{.}_{1}}\] The body is same therefore ?m? is constant. We know, \[K.E.=\frac{{{p}^{2}}}{2m}\] \[\Rightarrow K.E.\,\,\,\alpha \,\,{{P}^{2}}\] (\[\because \]?m? is same) \[\therefore \,\,K.E{{.}_{1}}=p_{1}^{2}\Rightarrow {{P}_{1}}=\sqrt{K.{{E}_{1}}}\] ?????(1) \[\,\,K.E{{.}_{2}}=P_{1}^{2}\Rightarrow \sqrt{K.{{E}_{2}}}\Rightarrow {{P}_{2}}=\sqrt{2K.E{{.}_{1}}}\] ?????(2) \[(\because \,\,K.E{{.}_{2}}=2K.{{E}_{1}})\] Dividing equation (2) by (1) we get, \[\frac{{{P}_{2}}}{{{P}_{1}}}=\frac{\sqrt{K.E{{.}_{1}}}}{\sqrt{2K.E{{.}_{2}}}}=\frac{1}{\sqrt{2}}\] \[\therefore \]Momentum is increaded by\[\sqrt{2}\]times.
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