Correct Answer - Option 2 : 2:1
CONCEPT:
- Kinetic energy is possed by a moving body and is given by
\(\Rightarrow KE = \frac{1}{2}MV^{2}\)
Where M = Mass, V = Velocity
- The relationship between the momentum and kinetic energy between the two bodies is given by
\(\Rightarrow P = \sqrt{2ME}\)
Where M = Mass of the particle, E = Kinetic energy
- The ratio between the momenta of two bodies is given by ( Which are having equal kinetic energy and different mass)
\(P_{1} = \sqrt{2M_{1}E}\) , \(P_{2} = \sqrt{2M_{2}E}\)
\(\Rightarrow\frac{P_{1}}{P_{2}} = \sqrt{\frac{M_{1}}{M_{2}}}\)
EXPLANATION:
- The ratio between the momenta of two bodies is given by ( Which are having equal kinetic energy and different mass)
\(P_{1} = \sqrt{2M_{1}E}\) , \(P_{2} = \sqrt{2M_{2}E}\)
\(\Rightarrow\frac{P_{1}}{P_{2}} = \sqrt{\frac{M_{1}}{M_{2}}}\)
Substituting the given values in the above equation
\(\Rightarrow \frac{P_{1}}{P_{2}} = \sqrt{\frac{16}{4}} = 4 :2=2:1\)
- Hence, option 2 is the answer
