Question

If force and displacement of the particle (in direction of force) are doubled. Then what will be the work?
A. Doubled
B. 4 times
C. Halved
D. \[\dfrac{1}{4}\] times

Answer 1

Hint:Before we start addressing the problem, we need to know about the displacement. When a force is applied, the object changes its position known as displacement. Since it is a vector quantity it has both direction and magnitude.

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

Complete step by step solution:
By the formula of work done, we know that,
\[W = \overrightarrow F \cdot \overrightarrow S \]
They have given that, suppose if the force and displacement is doubled what happens to the work done. As we know that the work done by a body is directly proportional to the force and displacement. If force and displacement become 2F and 2S then,
\[{W^1} = 2F \cdot 2S\]
\[\Rightarrow {W^1} = 4FS\]
\[\Rightarrow {W^1} = 4W\]
That is, if force and displacement are doubled, the work done will be 4 times.

To understand this we will consider an example where a force of 5N acts on a ball causing it to be displaced by a distance of 4m. we need to find the work required to cause this displacement.If we double the force then it will become 25N and similarly if we double the displacement, it will become 16m. Now, by using the formula to find the work done we have,
\[W = \overrightarrow F \cdot \overrightarrow S \]
\[\Rightarrow W = 5 \times 4\]
\[\Rightarrow W = 20J\]
Now,
\[{W^1} = 4W\]
\[\Rightarrow {W^1} = 4 \times 20\]
\[\therefore {W^1} = 60J\]
Therefore, when the force and displacement are doubled the work done will increase by 4 times.

Hence, option B is the correct answer.

Note: Since the work done of an object is directly proportional to the force applied and the displacement. A fixed change in either the force or displacement will lead to an equivalent change in work done.