Question

Assertion: The change in the kinetic energy of a particle is equal to the work done on it by the net force.
Reason: Change in kinetic energy of the particle is equal to the work only in case of a system of one particle.
A. Both assertion and reason are correct and the reason is the correct explanation for assertion
B. Both assertion and reason are correct but the reason is not the correct explanation for assertion
C. Assertion is correct but the reason is incorrect
D. Both assertion and reason are correct

Answer 1

Hint: Study about the work-energy theorem. It will help you answer the given question. The theorem says that the total work done on a particle is equal to the change in the kinetic energy of the particle. However, is the given reason explains the assertion?

Complete step-by-step solution:
From the work-energy theorem, we get that the total work done on a particle is equal to the change in the kinetic energy of the particle. We know that when work is, a net force is exerted on the particle. When a force is exerted on the particle, its velocity will change, and hence, the kinetic energy of the particle changes.
Here, the total work done is by all the forces (i.e. the work done by the net force) acting on the particle.
Therefore, from the theorem, we know that the change in the kinetic energy of a particle is equal to the work done on it by the net force.
The total work done by the net force acting on a system of particles is equal to the sum of works done on each particle by all the forces acting on each.
The work done on each particle will cause a change in the kinetic energy of each particle. The total change in kinetic energy of the system is the sum of the changes in kinetic energies of each particle.
Hence, we can say that a change in the kinetic energy of the system of particles is equal to the work done by the net force on the system.
i.e. $\Delta K=W$
Hence, the given assertion is correct. However, the reason for the assertion is incorrect as it does not explain the assertion.
Hence, the correct option is B.

Note: Many times it is misunderstood that the work-energy theorem is applicable only when the forces acting on the particles are conservative. However, this is a false condition. The work-energy theorem is true for all kinds of forces.