Work Power and Energy 1 Question 4
5. The work done on a particle of mass $m$ by a force, $K \frac{x}{\left(x^{2}+y^{2}\right)^{3 / 2}} \hat{\mathbf{i}}+\frac{y}{\left(x^{2}+y^{2}\right)^{3 / 2}} \hat{\mathbf{j}}$
$(K$ being a
constant of appropriate dimensions), when the particle is taken from the point $(a, 0)$ to the point $(0, a)$ along a circular path of radius $a$ about the origin in the $x-y$ plane is
(2013 Adv.)
(a) $\frac{2 K \pi}{a}$
(b) $\frac{K \pi}{a}$
(c) $\frac{K \pi}{2 a}$
(d) 0
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Answer:
Correct Answer: 5. (d)
Solution:
- $\mathbf{r}=\mathbf{O P}=x \hat{\mathbf{i}}+y \hat{\mathbf{j}}$
$$ \mathbf{F}=\frac{k}{\left(x^{2}+y^{2}\right)^{3 / 2}}(x \hat{\mathbf{i}}+y \hat{\mathbf{j}})=\frac{k}{r^{3}}(\mathbf{r}) $$
Since, $\mathbf{F}$ is along $\mathbf{r}$ or in radial direction.
Therefore, work done is zero.
