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