Question

The change in momentum of a body per unit time represents
A) Impulse
B) Acceleration
C) Kinetic Energy
D) Resultant force

Answer 1

Hint: The given problem can be explained on the basis of the concept of Impulse and momentum. The momentum describes the effect of the inertia of the moving particle. The impulse describes the effect of the force on a particle for a very small duration. The force that acts for a very small duration is called the impulsive force and the force that acts for considerable time is called the non-impulsive force.

Complete step by step answer:
Let us assume that a particle of mass m is moving with initial velocity u and after some time t, the velocity of the particle becomes v. The force that changes the speed of the particle from speed u to speed v is F.
The initial impulse of the particle is given as:
${P_i} = mu$
 The final impulse of the particle is given as:
${P_f} = mv$
The change in the momentum of the particle is given as:
$\Delta P = {P_f} - {P_i}......\left( 1 \right)$
Substitute the values of initial momentum${P_i}$ and final momentum ${P_f}$ in the expression to calculate the change in the momentum of the particle.
$\Delta P = mv - mu$
$\Delta P = m\left( {v - u} \right)......\left( 2 \right)$
The acceleration of the particle is given as:
$a = \dfrac{{v - u}}{t}$
The expression for the change in the momentum per unit time is given as:
$\dfrac{{\Delta P}}{t} = \dfrac{{m\left( {v - u} \right)}}{t}......\left( 3 \right)$
Substitute the value of the acceleration in the expression (3).
$\dfrac{{\Delta P}}{t} = ma......\left( 4 \right)$
The expression for the force on the particle is given as:
\[F = ma\]
Substitute the value of the force in the expression (4).
$\dfrac{{\Delta P}}{t} = F......\left( 5 \right)$
The expression of impulse of the particle is given as:
$I = F \cdot t$
$F = \dfrac{I}{t}$
Substitute the value of force in terms of impulse of the particle in the expression (5).
$\dfrac{{\Delta P}}{t} = \dfrac{I}{t}$
$\Delta P = I......\left( 6 \right)$
From the above expression (6), we can say that change in momentum is the same as the impulse of the particle.

Thus, the change in momentum of a body per unit time represents the impulse of the particle and the option (A) is the correct answer.

Note: Always remember that change in the momentum of the particle represents the impulse of the particle. The acceleration describes the variation in the velocity of the particle in certain duration. The kinetic energy of the particle is the same as the energy due to motion of the particle. The resultant force describes the net effect of all the force on the particle.