In physics, work is done when a force moves an object through some displacement. Work equals the force times the displacement in the direction of the force: W = F d cos theta, where theta is the angle between force and displacement. Memory hook: "No move, no work" - if the object does not move, or the force is perpendicular to the motion, the work is zero.
A force F acts at angle theta to the displacement d. Only the component along the motion, F cos theta, does work, giving W = F d cos theta.
Your doubts, answered
Is work done if the object does not move?
No. In physics, work needs displacement. If displacement is zero, W = F d cos theta = 0 no matter how large the force is. Pushing hard on a wall that does not move means zero work is done on the wall.
Why is holding a heavy bag not work in physics?
When you hold a bag still, your force is upward but there is no displacement. Since d = 0, work W = 0. Your muscles feel tired because of biology, but in physics no work is done on the bag.
What is the difference between everyday work and physics work?
In daily life, studying or thinking is called 'work'. In physics, work has a strict meaning: a force must act AND the object must move. Both a force and a displacement in the force's direction are needed, or the work is zero.
Can work be negative?
Yes. When the force and displacement point in opposite directions, theta = 180 degrees, so cos theta = -1 and work is negative. Friction and a braking force do negative work because they oppose the motion.
Why does cos theta come in the work formula?
Only the part of the force along the displacement does work. That component is F cos theta. So work = (F cos theta) times d = F d cos theta. If the force is perpendicular (theta = 90 degrees), cos 90 = 0 and no work is done.
⚠️ The NEET trap ✗ Any force applied on a body always does some work. ✓ Work is zero if there is no displacement (d = 0) or if the force is perpendicular to the displacement (theta = 90 degrees, cos 90 = 0). Force alone is not enough; motion along the force is needed. 🧠 NTA loves 'a coolie carries a bag on his head and walks' or 'a satellite in circular orbit' - in both the force is perpendicular to motion, so work = 0. Do not pick a non-zero value.
Real NEET questions
NEET 2016
A particle moves from point (-2 i + 5 j) to (4 j + 3 k) when a force (4 i + 3 j) N is applied. How much work is done by the force?
A · 2 J
B · 8 J
C · 11 J
D · 5 J ✓
Solution: Step 1: Find displacement S = final - initial = (0 i + 4 j + 3 k) - (-2 i + 5 j + 0 k) = 2 i - 1 j + 3 k. Step 2: Work is the dot product W = F . S = (4)(2) + (3)(-1) + (0)(3). Step 3: W = 8 - 3 + 0 = 5 J. Answer: D.
NEET 2017
A rain drop of mass 1 g falls from a height of 1 km and hits the ground with speed 50 m/s. Take g = 10 m/s^2. The work done by (i) gravity and (ii) the resistive force of air is:
A · (i) 1.25 J (ii) -8.25 J
B · (i) 100 J (ii) 8.75 J
C · (i) -10 J (ii) -8.25 J
D · (i) 10 J (ii) -8.75 J ✓
Solution: Step 1: Work by gravity W_grav = mgh = (10^-3 kg)(10)(10^3 m) = 10 J (force and motion are both downward, so positive). Step 2: Change in kinetic energy = (1/2) m v^2 = (1/2)(10^-3)(50^2) = 1.25 J. Step 3: Work-energy theorem: W_grav + W_air = change in KE, so W_air = 1.25 - 10 = -8.75 J (negative, since air resistance opposes motion). Answer: D.
Solved Work, Energy And Power NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The SI unit of work is the joule (J). One joule is the work done when a force of 1 newton moves an object 1 metre in the direction of the force. Work and energy share the same unit and dimensions [M L^2 T^-2].
Is work a scalar or a vector?
Work is a scalar quantity. It is the dot product of the force vector and the displacement vector, and a dot product always gives a scalar. Work has magnitude and sign (positive, negative or zero) but no direction.
What is the formula for work done by a constant force?
W = F d cos theta, where F is the force magnitude, d is the displacement magnitude, and theta is the angle between them. In vector form, W = F . d (the dot product of force and displacement).
When is work done maximum?
Work is maximum when the force acts fully along the displacement, that is theta = 0 degrees so cos 0 = 1 and W = F d. It becomes zero at theta = 90 degrees and negative (maximum in the opposite sense) at theta = 180 degrees.
