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The linear momentum of the body is increased by 30%. Calculate the percentile change in the kinetic energy of the particle if the mass of the particle is constant.
1. 50%
2. 69%
3. 39%
4. 55%

1 Answer

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Best answer
Correct Answer - Option 2 : 69%

CONCEPT:

  • The linear momentum of a body is the product of mass and velocity and is given by

⇒ P = m V

Where m = mass of the body and V = Velocity

  • Kinetic energy: The energy in a body due to its motion, is known as kinetic energy.
  • The relationship between the kinetic energy and linear momentum is given by

\(\Rightarrow Kinetic \ energy = \frac{P^{2}}{2m}\)

Where P = Momentum of the particle and M = mass of the particle 

CALCULATION

Given - The increase in linear momentum = 30 %, K = Initial kinetic energy, K1 = The new kinetic energy after the change in the momentum, P1 =The new momentum after the increase, and P = initial momentum

  • The percentage increase in the momentum can be  represented as

⇒ P1 = 1.30 P

  • The corresponding increase in the kinetic en energy is given by

\(⇒ K.E_{1} = \frac{P_{1}^{2}}{2M} = \frac{(1.30 P)^{2}}{2M} = \frac{1.69 P^{2}}{2M} =1.69 \frac{P^{2}}{2M}\)

\(⇒ K.E_{1} = 1.69 KE\)

  • The change in Kinetic energy is given by

⇒ ΔKE = KE1 - KE = 1.69 KE - KE = 0.69KE

  • The change can be expressed in percentile as

⇒ Change in percentile  = 0.69 × 100 = 69 %

  • Hence, option 2 is the answer

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