Consider two bodies of masses m₁ and m₂ moving with velocities v₁ and v₂respectively. 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:

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Consider two bodies of masses m₁ and m₂ moving with velocities v₁ and v₂respectively. 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:

momentum of 1^st body > momentum of 2^nd body
momentum of 1^st body < momentum of 2^nd body
both have equal momentum
no change in momentum

Answer 1

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 > m₂v₂
Which gives,

⇒ p₁ > p₂

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Question

Consider two bodies of masses m₁ and m₂ moving with velocities v₁ and v₂respectively. 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:

Answer (Detailed Solution Below)

Detailed Solution

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Consider two bodies of masses m1 and m2 moving with velocities v1 and v2 respectively. 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:

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Consider two bodies of masses m₁ and m₂ moving with velocities v₁ and v₂respectively. 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: