Question

In the case of negative work, the angle between the force and displacement is

• A. $0°$
• B. $45°$
• C. $90°$
• D. $180°$

Answer 1

The correct option is D

$180°$

The explanation for Correct Option:

Option (D):

1. Work done is defined as the force applied to displace a body from its original state.
2. Work done is a scalar quantity.
3. Force and displacement are vector quantities.
4. We know that the dot product of two vectors gives a scalar quantity as its result.
5. Therefore work done is the dot product of force and displacement.
6. Unit of work and energy and equal and it is termed as joules or $J$.

If $\overrightarrow{F}$ is the force applied and $\overrightarrow{S}$ is the displacement of the body, then the work done $W$ can be given as,

$W=\overrightarrow{F}.\overrightarrow{S}$

$=F.S.\cos \theta$

Where, $\theta$ is the angle between the direction of force vector and displacement vector.

Let $\theta =180°$

$FS\cos 180°=-FS=-W$, because $\cos 180°=-1$

Hence, if the angle is obtuse, work done is always negative.

The explanation for Incorrect Option:

Option (A):

Let $\theta =0°$

$\therefore FS\cos 0°=FS=W$

Option (B):

Let $\theta =45°$

$\therefore FS\cos 45°=\frac{FS}{\sqrt{2}}=\frac{W}{\sqrt{2}}$

Option (C):

Let $\theta =90°$

$\therefore FS\cos 90°=0$

Hence option D is the correct answer.