Gujarat BoardEnglish MediumSTD 9ScienceWork, Power And Energy1 Mark
MCQ
In case of negative work the angle between the force and displacement is:
A
$0^\circ$
B
$45^\circ$
C
$90^\circ $
✓
$180^\circ$
✓
Answer
Correct option: D.
$180^\circ$
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.
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.
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.
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 $180^\circ$.
$($i.e, force and displacement are anti parallel to each other$)$ So, it is true.
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