Question

A force F = - K $(y\hat{i}+x\hat{j})$ (where K is a positive constant) acts on a particle moving in the x-y plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0), and then parallel to the y-axis to the point (a, a). The total work done by the force F on the particle is

• A. $-2K{a}^2$
• B. $2K{a}^2$
• C. $-K{a}^2$
• D. $K{a}^2$

Answer 1

Answer: (C)

$-K{a}^2$

$F=-K(y\hat{i}+x\hat{j})$

$W_1=F.ds$

$=-K(y\hat{i}+x\hat{j}).a\hat{i}$

$=-Kya$

$W_2=-K(y\hat{i}+x\hat{j}).a\hat{j}$

$=-Kxa$

Total work done

$=W_1+W_2$

$=-Ka(y+x)$

Putting the value of $x$ and $y$

$W=-K{a}^2$