A) doubled
B) tripled
C) increase 9 times
D) increase 15 times
Correct Answer: C
Solution :
Given, \[{{v}_{1}}=v\,\,m/s\,\,\,{{v}_{2}}=3\,\,m/sK.E.=?\] We know, \[K.E.=\frac{1}{2}m{{V}^{2}}\] \[\Rightarrow K.E.\propto {{v}^{2}}\](\[\because \]The body is same therefore ?m? is constant) \[\therefore \,\,K.E{{.}_{1}}={{v}_{2}}\] ???..(1) and \[K.E{{.}_{2}}={{(3v)}^{2}}=9{{v}^{2}}\] ???..(2) Dividing equation (2) by (1) we get, \[\frac{K.{{E}_{2}}}{K.{{E}_{1}}}=\frac{9{{v}^{2}}}{{{v}^{2}}}=\frac{9}{1}\] \[\therefore \,\,K.{{E}_{2}}:\,K.{{E}_{1}}=9:1\] Therefore, K.E is increases 9 times.
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