Question

If the force and displacement of a particle in direction of force are doubled. Work would be

• A. Double
• B. $4$ times
• C. Half
• D. $\frac{1}{4}$ times

Answer 1

The correct option is B

$4$ times

Step 1 Given data:

The force($\mathrm{F}$) and displacement ($\mathrm{S}$)of a particle in direction of force are doubled. That is,

$\mathrm{F}\text{'}=2\times \mathrm{F}$

$\mathrm{S}\text{'}=2\times \mathrm{S}$

Step 2 Formula used:

Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.

That is, $\mathrm{W}=\mathrm{F}\times \mathrm{S}$

Step 3 Work:

The work of a particle in the direction of force is,

$\mathrm{W}=\mathrm{F}\times \mathrm{S}....\left(1\right)$

Here, the force($\mathrm{F}$) and displacement ($\mathrm{S}$)of a particle in the direction of force are doubled,

Therefore the new work is,

$$\begin{gathered} \mathrm{W}\text{'}=2\times \mathrm{F}\times 2\times \mathrm{S} \\ \mathrm{W}\text{'}=4\times \mathrm{F}\times \mathrm{S}....\left(2\right) \end{gathered}$$

Substituting equation (1) in equation (2),

$\mathrm{W}\text{'}=4\times \mathrm{W}$

Therefore, if the force and displacement of a particle in direction of force are doubled then the work would be $4$ times. Hence, option B is correct.