x-y nbsp; સમતલ માં ગતિ કરતાં એક કણ પર બળ

For motion of the particle from $(0, 0)$ to $(a, 0)$

$\overrightarrow F = - K(0\,\hat i + a\,\hat j)$ $ \Rightarrow \,\,\overrightarrow F = - Ka\hat j$

Displacement $\overrightarrow {r\,} = (a\,\hat i + 0\,\hat j) - (0\,\hat i + 0\,\hat j) = a\hat i$

So work done from $(0, 0)$ to $(a, 0)$ is given by

$W = \overrightarrow F \,.\,\overrightarrow {r\,} $$ = - Ka\hat j\,.\,a\hat i = 0$

For motion $(a, 0)$ to $(a, a)$

$\overrightarrow F = - K(a\hat i + a\hat j)$ and displacement

$\overrightarrow {r\,} = (a\hat i + a\hat j) - (a\hat i + 0\hat j) = a\hat j$

So work done from $(a, 0)$ to $(a, a)$ $W = \overrightarrow F \,.\,\overrightarrow {r\,} $

$ = - K(a\hat i + a\hat j)\,.\,a\hat j = - K{a^2}$

So total work done$ = - K{a^2}$