question_answer

Two bodies of equal masses move with uniform velocity v and 2v respectively. Find the ratio of their kinetic energies.                

Answer:

Body-1	Body-2
\[{{m}_{1}}=m\]	\[{{m}_{2}}=m\]
\[{{v}_{1}}=v\]	\[{{v}_{2}}=2v\]

We know, \[K.E.=\frac{1}{2}m{{v}^{2}}\] Applying the above formula for two cases, we get \[\Rightarrow \]                                               ?????(1) \[K.E.=\frac{1}{2}\times m\times {{(2v)}^{2}}=2m{{V}^{2}}\]       ?????(2) Dividing equation. (2) by (1), we get \[\frac{K.{{E}_{1}}}{K.{{E}_{2}}}=\frac{\frac{1}{2}m{{v}^{2}}}{2m{{v}^{2}}}=\frac{m{{v}^{2}}}{4m{{v}^{2}}}=\frac{1}{4}\] \[\therefore K.E{{.}_{1}}:K.E{{.}_{2}}=1:4\]