Q.A body is moved along a closed loop. Is the work done in moving the body necessarily zero? If not, state the condition under which work done over a closed path is always zero.

The key idea is that work done by a force over a closed path depends on whether the force is conservative or non-conservative.

For a conservative force (like gravity or electrostatic force), the work done depends only on the initial and final positions, not on the path taken. Since a closed loop returns to the starting point, the net displacement is zero, so the work done by a conservative force over any closed path is always zero. …

The question touches a fundamental idea in physics: the nature of forces and how they transfer energy. When you move a body along a closed loop — starting and ending at the same point — the work done by a force can be zero or non‑zero, depending entirely on the type of force.

Let’s unpack this.

1. What does “work over a closed loop” mean?

   You take an object from point A, move it along some path that eventually brings it back to A. The total work done by a given force during that round trip is what we’re asking about. If the force is conservative, the work depends only on the start and end points — and since they’re the same, the net work is zero. If the force is non‑conservative, the work depends on the path itself, so a closed loop can have non‑zero work.

2. The key distinction: conservative vs. non‑conservative forces

   A conservative force has a special property: you can define a potential energy for it. Gravity, electrostatic force, and spring force are classic examples. For these, the work done around any closed path is exactly zero.

   A non‑conservative force, like friction or air resistance, has no associated potential energy. The work it does depends on how far and along what route you move — so going around a closed loop, friction always does negative work (it dissipates energy as heat), and the total is not zero.

3. Why does this happen physically?

   Imagine sliding a book across a table and back to its starting point. Gravity (conservative) does zero net work — the book goes down and up, energy is stored and returned. But friction (non‑conservative) does negative work the whole way; you have to keep pushing, and the book’s kinetic energy is lost as heat. The round trip costs energy, so work is not zero.

4. The condition for zero work over a closed path …

Concept: Work Over a Closed Path — Conservative vs Non-Conservative Forces

Zero net displacement does not automatically mean zero work; whether

the round-trip work vanishes depends entirely on whether the force is

conservative.

Step 1: Case of a conservative force

For a conservative force (e.g. gravity, spring force, electrostatic force),

work done depends only on the start and end points, not on the path taken.

Since a closed loop starts and ends at the same point:

Step 2: Case of a non-conservative force

For a non-conservative force (e.g. friction, air drag), the work done

depends on the actual path length travelled, not just the endpoints. Such a

force (friction, for instance) always opposes motion, so it keeps doing

negative work all the way around a closed loop — the total is not zero.

Step 3: Physical illustration

Sliding a book across a table and back: gravity does zero net work (down

then up, cancels exactly), but friction does negative work throughout the …