Question

If F and S are force and displacement
respectively, the work done is zero if-
(1) F and S are opposite in direction
(2) F and S are in same direction
(3) F and S are mutually perpendicular
(4) F is greater than Ś​

Answer 1

Work done is said to be Zero , in either of the 2 case :

• Force applied should be zero
• Work then should be zero.

Answer + Explaination

When Force applied and Displacement are mutually perpendicular to each other then the work done will be zero.

As , W = Force × Displacement

Angle angle will be 90° ( perpendicular)

So putting the required values we get ,

W = F × S COS 90°

(cos 90° = 0 )

Therefore ,

W = 0

Hence no work is done in this situation

Correct answer

Option

3) F and S are mutually perpendicular .

Let's have a quick glance at the remaining options :

1) F and S are opposite in direction

Here work done will be negative

As , Cos 180° = -1

Hence work done comes out to be negative

2) F and S are in same direction.

Means cos 0°

W = Force × Displacement

W = 1

So this option is not applicable coz work done won't be equal to 0.

4) F is greater than S

However this option could be easily eliminated as F > S won't produce and answer equal to zero.Because if a force of knights magnitude is applied means definitely displacement will occur hence work is said to be done.

Answer 2

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

On a body a force of "F" acts and produces a displacement "S".

$\huge{\bold{\underline{Explanation:-}}}$

Let's find out it by hit and trail method I.e. verifying each option.

• Case-1

F and S are in opposite direction.

since, they are in opposite direction the angle between them is 180°.

Now, substituting in work done formula.

$\large{\bold{\boxed{\boxed{ W = F.S. \cos \theta}}}}$

${ \to W = F.S \cos180}$

${ \to W = - F.S}$ as cos 180° = -1.

So,the work done here is negative but not zero.

• Case-2

F and S are in same direction.

since, they are in same direction the angle between them is 0°.

Now, substituting in work done formula.

$\large{\bold{\boxed{\boxed{ W = F.S. \cos \theta}}}}$

${ \to W = F.S \cos0}$

${ \to W = F.S}$ as cos 0° = 1.

So,the work done here is positive but not zero.

• Case-3

F and S are mutually perpendicular.

since, they are in opposite direction the angle between them is 90°.

Now, substituting in work done formula.

$\large{\bold{\boxed{\boxed{ W = F.S. \cos \theta}}}}$

${ \to W = F.S \cos90}$

${ \to W = 0}$ as cos 90° = 0.

So,the work done by the Force here is zero.

• Case-4

F is greater than S.

As the force is greater than displacement

So, the scalar product will give a positive value.Then this is not the case.

So, the work done produced here is

${W = F.S.}$

So,the work done by the force is positive.

Therefore, the third option has work done = 0.

So, the answer is 3rd option which that Force and displacement are mutually perpendicular to each other.