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If two bodies of different masses have the same kinetic energy, which body mass will have more momentum?
1. The body with more mass will have more momentum
2. the body with less mass will have more momentum
3. Both the bodies will have the same momentum
4. Nothing can be said about momentum

1 Answer

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Correct Answer - Option 1 : The body with more mass will have more momentum

CONCEPT:

  • Momentum: A property of a body in motion that is equal to the product of the body's mass and velocity is called momentum.

P = mv

where P is the momentum of the body, m is the mass of the body, and v is the velocity of the body.

  • Kinetic energy: The energy in a body due to its motion, is known as kinetic energy.

The kinetic energy in terms of momentum is given by:

\(K=\frac{P^2}{2m}\)

where K is the kinetic energy of the body, P is the momentum of the body and m is the mass of the body.

EXPLANATION:

Given that the Kinetic energy of both masses is the same. 

K1 = K2

\(\frac{P_1^2}{2M_1}=\frac{P_2^2}{2M_2}\)

\(\frac{P_1^2}{P_2^2}=\frac{2M_1}{2M_2}\)

\(\frac{P_1^2}{P_2^2}=\frac{M_1}{M_2}\)

P2 ∝ M

P ∝ √M

So the more mass will give the more momentum.

Hence the correct answer is option 1 i.e. The body with more mass will have more momentum

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