Question

A body of mass 10 kg is dropped to the ground from a height of 10 meters. Find the work done by the gravitational force. Given that\[\left( {g = 9.8m{s^{ - 2}}} \right)\]
A. -490 joules
B. +490 joules
C. -980 joules
D. +980 joules

Answer 1

Hint:Before going to solve this question we need to understand the work done and the work-energy theorem. Work is nothing but a force needed to move an object from one place to another. The work-energy theorem states that the work done by the force is stored in a system in the form of energy. Work done can be positive, negative, or zero depending on the angle between the force applied and the displacement.

Formula Used:
The formula to find the work done is,
\[W = \overrightarrow F \cdot \overrightarrow S \]……… (1)
Where, \[\overrightarrow F \] is force applied and \[\overrightarrow S \] is displacement.

Complete step by step solution:
They have a body of mass 10 kg and are dropped to the ground from a height of 10 meters. Then we need to find the work done by the gravitational force.
Given \[\left( {g = 9.8\,m{s^{ - 2}}} \right)\]
From the equation (1), the formula for the work done is,
\[W = \overrightarrow F \cdot \overrightarrow S \]
\[\Rightarrow W = mg \times h\]
Here, \[\overrightarrow F = mg\]and the displacement is nothing but the height h.

Then, \[W = 10 \times 9.8 \times 10\]
\[ \Rightarrow W = 980J\]
Since, the body is moving in the direction of force, the work done by gravitational force will be positive i.e.,
\[ \therefore W = + 980J\]
Therefore, the work done by the gravitational force is +980 J.

Hence, option D is the correct answer.

Note: Consider an object, when it falls freely towards the surface of earth from a certain height, its velocity changes and this change in velocity produces acceleration in the object which is called acceleration due to gravity and is denoted by g.