Work And Energy — Science STD 9 — Question

4. 180°.

Explanation:

1. Work done W = F.d $\cos\theta$

$\therefore$ Work done at $\theta=0^\circ,\ \text{W}=\text{F.d}\ \cos0^\circ$ $(\therefore\cos0^\circ=1)$

$\Rightarrow$ W = F.d

For angle $\theta=0^\circ,$

Work done Is positive, so it is not true.

2. We know that work done, W = F.d $\cos\theta$

$\text{W}=\text{F.d}\ \cos45^\circ$ $\Big(\because\cos45^\circ=\frac{1}{\sqrt{2}}\Big)$

$\text{W}=\frac{\text{F.d}}{\sqrt{2}}$

For angle $0=45^\circ,$

work done is positive, so it is not true.

3. We know that work done, W = d $\cos\theta$

Work done at $\theta=90^\circ,$ W = F.d $\cos90^\circ$ $(\therefore\cos90^\circ=0)$

W = 0

So, it in not true.

4. Work done at $\theta=180^\circ,\ \text{W}=\text{F.d}\ \cos\theta\ \ (\therefore\cos180^\circ=-1)$

W = -F.d

For negative work, the angle between the force and displacement should be 180°.

(i.e, force and displacement are anti parallel to each other) So, it is true.