The linear momentum of a particle is increased by 25% then find the increment in the kinetic energy if the mass of the particle is constant.

Question

Question

This question was previously asked in

Airforce Group X 5 November 2020 Memory Based Paper

Answer 1

The correct option is 3.

CONCEPT:

Momentum: A property of a body in motion that is equal to the product of the body's mass and velocity is called momentum.

P = mv

where P is the momentum of the body, m is the mass of the body, and v is the velocity of the body.

Momentum Conservation: When in a system, there is no external force then the total momentum (P) of the system will be conserved.
Kinetic energy: The energy in a body due to its motion, is known as kinetic energy.

The kinetic energy in terms of momentum is given by:

$K = \frac{P^{2}}{2 m}$

where K is the kinetic energy of the body, P is the momentum of the body and m is the mass of the body.

CALCULATION:

$K = \frac{P^{2}}{2 M}$

Let initial value of P = 100, m = 100

After increase of 25% P = 125

Initial kinetic energy $K_{i} = \frac{P_{i}^{2}}{2 m} = \frac{100^{2}}{2 \times 100} = 50$

Final kinetic energy $K_{f} = \frac{P_{f}^{2}}{2 m} = \frac{125^{2}}{2 \times 100} = 78.125$

% Increase in Kinetic energy = $\frac{(K_{f} - K_{i})}{K_{i}} \times 100 = \frac{(78.125 - 50)}{50} \times 100 = 56.25$ %