Question

Work done by the gravitational force on a body of mass $m$ moving on a smooth horizontal surface through a distance $s$ is: (Given acceleration due to gravity $= g$):
a. $mgs$
b. $- mgs$
c. $0$
d. $2mgs$

Answer 1

Work done by a force is defined as the product of the magnitude of the force and the displacement of the object. When an object falls towards the earth, the work is done by gravity in the downward direction, whereas if the object moves up, the work is done by the object against gravity.

Complete step by step answer:
The gravitational force of earth acts on all objects present on its surface, when an object moves up or falls down, some work is done.
When it goes upwards, the work is done by the object against gravity because the direction of the motion of the object is opposite to the direction of gravitational force. To represent the work done by the gravitational force, in this case, we put a negative sign with the magnitude. Therefore, the magnitude, in this case, will be,
$W = - mgs$

When the object falls towards the earth, it travels in the direction of gravitational force and thus the work is done by gravity. To represent the work done by the gravitational force, in this case, we can write-
$W = mgs$

But if an object moves in the horizontal direction, gravity does not affect its motion (unless there is friction). Thus, for an object moving in the horizontal direction the work done by gravity would be zero.

Hence, the correct answer is option (C).

Note: The force of gravity only acts in the vertical direction, it does not affect the horizontal motion of an object. Therefore, if an object moves in the horizontal direction, the work done by the gravitational force is zero. However, if the object moves up and down, there will be work done by or against gravity.