Question

Consider two bodies of masses m₁ and m₂ moving with velocities v₁ and v₂ respectively. Where 2^nd 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 1^st body > momentum of 2^nd body
2. momentum of 1^st body < momentum of 2^nd body
3. both have equal momentum
4. no change in momentum

Answer 1

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

The correct answer is option 1) i.e. momentum of 1^st body > momentum of 2^nd 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 = m₁ × 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 > m₂ v₂
Which gives p₁ > p₂