Question

A 4 kg mass and 1 kg mass are moving with equal linear momenta. The ratio of their kinetic energies is

• A. 1: 2
• B. 2 : 1
• C. 1 : 4
• D. 4 : 1

Answer 1

The correct option is C 1 : 4

$Linearmomentum\left(p\right)=Mass\times velocity=MVKineticenergy\left(E\right)=\frac{1}{2}M{V}^{2}Let,Velocityof1kgmassisVand4kgis{V}^{\prime }pfor1kgmass=pfor4kgmass1\times V=4\times V^{\prime }So,V^{\prime }=\frac{V}{4}Now,Efor1kgmass=\frac{1}{2}1\times V^2=\frac{1}{2}{V}^{2}and{E}^{\prime }for4kgmass=\frac{1}{2}M{V}^{{}^{\prime }2}=\frac{1}{2}4\times {\left(\frac{V}{4}\right)}^2{E}^{\prime }=\frac{1}{2}4\times \left(\frac{V}{4}\right)\times \left(\frac{V}{4}\right)=\frac{1}{2}{V}^2\times \frac{1}{4}=\frac{E}{4}{E}^{\prime }=\frac{E}{4}\frac{E^{\prime }}{E}=\frac{1}{4}{E}^{\prime }:E=1:4$