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Consider two bodies of masses m1 and m2 moving with velocities v1 and vrespectively. Where 2nd body has a higher velocity than the first one. Also, they both have equal kinetic energies. Then, which of the following option holds true for the situation:
1. momentum of 1st body > momentum of 2nd body
2. momentum of 1st body < momentum of 2nd body
3. both have equal momentum
4. no change in momentum

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Correct Answer - Option 1 : momentum of 1st body > momentum of 2nd body

The correct answer is option 1) i.e. momentum of 1st body > momentum of 2nd body

CONCEPT:

  • Kinetic energy (KE): The energy due to the motion of the body is called kinetic energy.

KE = (1/2) m v2

  • Momentum (p): The product of mass and velocity is called momentum.

p = m v

Where m is mass and v is velocity

EXPLANATION:

K1 = (1/2) m1 v12

K2 = (1/2) m2 v22 

Given that:

The kinetic energies of objects A and B are equal.
K1 = K2 
The momenta of objects A and B:

p1 = m× v1 and

p2 = m2 × v2

We know that
v1 < v2
Divide the numerator and denominator in the above by K1 and K2 (note K1 = K2), to obtain

v1/K1 < v2/K2

Which gives
K1/v1 > K2/v2
Substitute K1 and K2 by their expressions given above
(1/2) m1 v12 / v1 > (1/2) m2 v22 /v2
Simplify to obtain
m1v1 > mv2
Which gives p1 > p2

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