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Question
A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has larger kinetic energy?
Solution
Let m and M be the masses of light and a heavy object moving with velocities v and V respectively.
As both have the same momentum,
∴ mv = MV
or `"M"/"V'` .........(i)
The kinetic energy of a light object,
`"K"_"m" = 1/2 "mv"^2`
The kinetic energy of a heavy object,
`"K"_"m' = 1/2 "mV"^2`
The kinetic energy of a heavy object,
`"K"_"M" = 1/2 "MV"^2`
∴ `("K"_"m")/("K"_"m") = (1/2 "mv"^2)/(1/2 "MV"^2)`
= `"m"/"M" xx ("M"/"m")^2`
= `"M"/"m"` (Using (i))
As M>m;
Km > KM, i.e. light object has larger kinetic energy.
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