Question

Assertion:
Work done by a constant force is path independent
Reasoning:
All constant forces are conservative in nature
(A). both assertion and reason is correct and reason is correct explanation for assertion
(B). both assertion and reason are correct but reason is not the correct explanation for assertion
(C). assertion is correct but reason is incorrect
(D). both assertion and reason are incorrect

Answer 1

Hint: Work done by an object is the product of force and displacement. It is a scalar quantity while conservative forces do not depend on the path taken but on the initial and final states. Constant force acting on an object has a fixed magnitude throughout and conservative forces are path independent.

Complete Answer:
The work done by a force is the product of magnitude of force and the displacement covered by the object. Work done, $W$ by an object is given by-
$W=\vec{F}\cdot \vec{x}$
Here, $\vec{F}$ is the force vector acting on the object
$\vec{x}$is the displacement vector
Since work done is the dot product of two vectors, it is a scalar quantity. That is why it does not depend on the path taken but only depends on the initial and final states of the object. Therefore, the assertion is correct.
A conservative force is force acting on the object which does not depend on the path but rather depends on the initial and final states of the object
But all constant forces are not conservative in nature. For example- frictional force is constant but it is not conservative in nature. Therefore reasoning is incorrect.
As work is path independent and constant forces are not always conservative, our assertion is correct and reasoning is wrong.

Therefore, the correct option is (C).

Note:
Frictional force is the force that opposes the motion of an object. When the object is on rest, its value increases upto a certain magnitude after which it becomes constant when the object starts moving. In case of conservative forces, when an object changes its position the force also changes its potential energy.