question_answer

Two objects having equal masses are moving with uniform velocities of 2 m/s and 6 m/s respectively. Calculate the ratio of their kinetic energies?

Answer:

               

Body-1	Body-2
\[{{m}_{1}}=m/s\]	\[{{m}_{2}}=m\,kg\]
\[{{v}_{1}}=2\,\,m/s\]	\[{{v}_{2}}=6\,\,m/s\]

We know, \[K.E.=\frac{1}{2}m{{v}^{2}}\] Applying the above formula for both cases, we get \[K.E{{.}_{1}}=\frac{1}{2}\times m\times {{(2)}^{2}}=2m\]            ????..(1) \[K.E{{.}_{2}}=\frac{1}{2}\times m\times {{(6)}^{2}}=18m\]          ????..(2) Dividing equation (1) by (2), we get \[\frac{K.E{{.}_{1}}}{K.E{{.}_{2}}}=\frac{2m}{18m}=\frac{1}{9}\] Therefore, \[K.E{{.}_{1}}:K.E{{.}_{2}}=1:90\]