Question

The momenta of two particles of masses m and 2m are 2p and p respectively. The ratio of their kinetic energies will be

• A. 2:01
• B. 4:01
• C. 1:08
• D. 8:01

Answer 1

Answer: (D)

8:01

Answer 2

$K=\frac{1}{2}m{{v}^{2}}=\frac{{{p}^{2}}}{2m}$ $\therefore$ $\frac{{{K}_{1}}}{{{K}_{2}}}={{\left( \frac{{{p}_{1}}}{{{p}_{2}}} \right)}^{2}}.\left( \frac{{{m}_{2}}}{{{m}_{1}}} \right)$ $\frac{{{K}_{1}}}{{{K}_{2}}}={{\left( \frac{2p}{p} \right)}^{2}}.\left( \frac{2m}{m} \right)=\frac{8}{1}$