# An object is displaced from position vector $\vec{r_{1}}&space;=&space;(2\hat{i}+3\hat{j})m$ to $\vec{r_{2}}&space;=&space;(4\hat{i}+6\hat{j})m$ under a force $\vec{F}&space;=&space;(3x^{2}\hat{i}+2y\hat{j})N$ then work done by the force is

(a) 24 J

(b) 33 J

(c) 83 J

(d) 45 J

Work done is given by,

$$\begin{array}{l}W = \int \vec{F}.(dx\hat{i}+dy\hat{j})\end{array}$$

$$\begin{array}{l}W = \int_{2}^{4}3x^{2}dx + \int_{3}^{6}2ydy\end{array}$$

$$\begin{array}{l}W = \left [ x^{3} \right ]_{2}^{4}+\left [ y^{2} \right ]_{3}^{6}\end{array}$$

W = (64 – 8) + (36 – 9)

W = 56 + 27

We get,

W = 83 J

Hence, the correct option is (c)