$2$ particles of mass $1$ kg and $5$ kg have same momentum, calculate ratio of their K.E:

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Solution

We can relate kinetic energy and momentum of an object by the given equation, $K_{E} = \frac{p^{2}}{2 m}$
As the momentum of both the objects are same i.e $p_{1} = p_{2}$
$\frac{K_{E 1}}{K_{E 2}} = \frac{\frac{p_{1}^{2}}{2 m_{1}}}{\frac{p_{2}^{2}}{2 m_{2}}} = \frac{m_{2}}{m_{1}} = \frac{5}{1}$

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2 particles of mass 1kg and 5kg have same momentum, calculate ratio of their K.E:

We can relate kinetic energy and momentum of an object by the given equation,KE=p22m As the momentum of both the objects are same i.e p1=p2KE1KE2=p212m1p222m2=m2m1=51

$2$ particles of mass $1$ kg and $5$ kg have same momentum, calculate ratio of their K.E:

We can relate kinetic energy and momentum of an object by the given equation, $K_{E} = \frac{p^{2}}{2 m}$
As the momentum of both the objects are same i.e $p_{1} = p_{2}$
$\frac{K_{E 1}}{K_{E 2}} = \frac{\frac{p_{1}^{2}}{2 m_{1}}}{\frac{p_{2}^{2}}{2 m_{2}}} = \frac{m_{2}}{m_{1}} = \frac{5}{1}$