question_answer

A horse and a dog are running with the same speed. If the mass of the horse is ten times that of the dog, then what is the ratio of their kinetic energies?

Answer:

               

Dog	Horse
mass \[({{m}_{1}})=m\]	mass \[({{m}_{2}})=10\,m\]
speed \[({{V}_{1}})=V\]	speed \[({{V}_{2}})=V\]

We know, \[K.E.\frac{1}{2}m{{v}^{2}}\] Applying the above formula for two cases, we get \[K.E{{.}_{1}}\frac{1}{2}m{{v}^{2}}\]                                        ???..(1) \[K.E{{.}_{2}}=\frac{1}{2}\times 10m\times {{v}^{2}}m=5m{{v}^{2}}\]     ???..(2) Dividing equation (1) by (2) we get \[\frac{K.E{{.}_{1}}}{K.E{{.}_{2}}}=\frac{\frac{1}{2}m{{v}^{2}}}{5m{{v}^{2}}}=\frac{1}{10}\] \[\therefore \,\,K.E{{.}_{1}}:K.E{{.}_{2}}=1:10\]