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Two bodies having masses 16 Kg and 4 Kg have equal kinetic energy. What will be the ratio of their momentum?
1. 3:2
2. 2:1
3. 5:1
4. 2:3

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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

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