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
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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