JEE Main Syllabus 2025 PDF - Subject Wise Topics

# Work Done By A Constant Force - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

## Quick Facts

• Nature of Work Done is considered one of the most asked concept.

• 11 Questions around this concept.

## Solve by difficulty

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that :

A force   $\inline \vec{F}= \left ( 5\hat{i} +3\hat{j}+2\hat{k}\right )N$    is applied over a particle which displaces it from its origin to the point $\inline \vec{r}= \left ( 2\hat{i} -\hat{j}\right )m$ . The work done on the particle in joule is :

## Concepts Covered - 2

Work done by a constant force
• Work-

Work is said to be done when a force applied on the body displaces the body through a certain distance along the direction of the force.

•  Work done by a constant force-

1. The scalar product of the force vector ($\underset{F}{\rightarrow}$) and the displacement vector ($\underset{S}{\rightarrow}$)

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

1. The product of the magnitude of force $\left ( F \right )$magnitude of displacement $\left (S \right )$ and cosine of the angle between them  $\left (\Theta \right )$

$W=FS\cos \Theta$

1. If the number of forces   $\vec{F}_{1},\vec{F}_{2},\vec{F}_{3} ......,\vec{F}_{n}$, are acting on a body and it shifts from position vector $\vec{r_1}$ to position vector $\vec{r_2}$

Then $W=\left(\vec{F}_{1}+\vec{F}_{2}+\vec{F}_{3} \ldots \ldots \ldots+\vec{F}_{n}\right) \cdot\left(\vec{r}_{2}-\vec{r}_{1}\right)=\vec{F}_{n e t} \cdot \vec{r}_{n e t}$

1.  Units-

• SI Unit-Joule

• CGS Unit- Erg

• $1 \ Joule = 10^7 Erg$

1. Dimension- $ML^2T^{-2}$

2. Dependence of work done by a constant force

1. Frame of reference

With a change of frame of reference (inertial) force does not change while displacement may change. So the work done by a force will be different in different frames.

i.e. A person is pushing a box inside a moving train with a force  $\vec{F}$

Displacement inside train $\vec{S}$

Displacement of the train in the ground frame is $\vec{S}_{0}$

Then work done by the force $\vec{F}$ is   $W= \vec{F}\cdot \left ( \vec{S}+\vec{S_{0}} \right )$

Nature of Work Done

1. Positive Work-

• Positive work means that force (or its component) is parallel to displacement.

• Means $0\leq \Theta < \frac{\pi }{2}$

Where $\Theta$ is the angle between force vectors and displacement vector

• Maximum work = $W_{max} = FS,\ When\ \theta = 0^{0}$

• E.g When you move a block by pulling it then work done by you on the block is positive

1. Negative Work

• Negative work means that force (or its component) is opposite to displacement.

• Means $\frac{\pi }{2}< \Theta \leq \pi$

Where $\Theta$ is the angle between force vectors and displacement vector

• Minimum work= $W_{min} = -FS,\ When\ \theta = 180^{0}$

• E.g When a body is made to slide over a rough surface, the work done by the frictional force is negative

1. Zero work

• Under three condition Work can be zero

a. If the force is perpendicular to the displacement

Means $\Theta = \frac{\pi }{2}$

E.g-When a body moves in a circle the work done by the centripetal force is always zero.

b. If there is no displacement (means s = 0)

E.g- When a person tries to displace a wall by applying a force and can't able to move the wall

So the work done by the person on the wall is zero.

c. If there is no force acting on the body (means F=0)

E.g-Motion of an isolated body in free space.

## Study it with Videos

Work done by a constant force
Nature of Work Done

"Stay in the loop. Receive exam news, study resources, and expert advice!"