Question #a5d68

Mar 17, 2016

C

Explanation:

Work done $= \vec{F} \cdot \vec{x}$,
When force $\vec{F}$ moves through a distance $\vec{x}$

It is true that physically distance moved by weight is along the direction of $\vec{r}$. The weight $W$ is due to force of gravity and is acting in the downwards direction.

From the picture $\vec{r}$ can be resolved into its $x \mathmr{and} y$ components,
$\vec{r} = \vec{p} + \vec{q}$
Work done $= - \vec{W} \cdot \vec{r} = - \vec{W} \cdot \left(\vec{p} + \vec{q}\right)$
we know that in a dot product for $\theta = {90}^{\circ}$, $\cos \theta = 0$. Therefore, first part $\vec{W} \cdot \vec{p} = 0$
We obtain work done $= - \vec{W} \cdot \vec{q} = - | \vec{W} | \cdot | \vec{q} | \cos \theta$
Angle between the two is ${180}^{\circ} \mathmr{and} \cos {180}^{\circ} = - 1$
Hence the result.