Question

Two bodies of masses $m$ and $2m$ have same momentum. Their respective kinetic energies $E1$ and $E2$ are in the ratio

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

Answer 1

The correct option is C $2:1$

Let velocity of body with m mass=V

Let velocity of body with 2m mass=V'

Let kinetic energy of m mass be E1

and kinetic energy 2m mass be E2

Given, Linear momentum of body with m mass = Linear momentum of body with 2m mass

$Linearmomentum\left(m\right)=Mass\times velocity=MVKineticenergy\left(E\right)=\frac{1}{2}M{V}^{2}mV=2m{V}^{\prime }So,V=2V^{\prime }E1=\frac{1}{2}{mV}^{2}andE2=\frac{1}{2}2m{V}^{{}^{\prime }2}E1=\frac{1}{2}m{\left(2V^{\prime }\right)}^2=\frac{1}{2}2m{V}^{{}^{\prime }2}\times 2=E2\times 2So\frac{E1}{E2}=2$