SATHEE: Work Power and Energy 1 Question 4

Work Power and Energy 1 Question 4

5. The work done on a particle of mass $m$ by a force, $K \frac{x}{{(x^{2} + y^{2})}^{3 / 2}} \hat{i} + \frac{y}{{(x^{2} + y^{2})}^{3 / 2}} \hat{j}$

$(K$ 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) $\frac{2 K π}{a}$

(b) $\frac{K π}{a}$

(c) $\frac{K π}{2 a}$

(d) 0

Show Answer

Answer:

Correct Answer: 5. (d)

Solution:

$r = O P = x \hat{i} + y \hat{j}$

$F = \frac{k}{{(x^{2} + y^{2})}^{3 / 2}} (x \hat{i} + y \hat{j}) = \frac{k}{r^{3}} (r)$

Since, $F$ is along $r$ or in radial direction.

Therefore, work done is zero.

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Work Power and Energy 1 Question 4

5. The work done on a particle of mass m by a force, Kx(x2+y2)3/2i^+y(x2+y2)3/2j^

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5. The work done on a particle of mass $m$ by a force, $K \frac{x}{{(x^{2} + y^{2})}^{3 / 2}} \hat{i} + \frac{y}{{(x^{2} + y^{2})}^{3 / 2}} \hat{j}$