Understanding Work Done by a Moment

In physics, work is done when a force causes displacement. In linear motion, the work done \(W\) by a constant force \(F\) acting over a displacement \(d\) is given by \(W = F \cdot d\), assuming the force and displacement are in the same direction.

Rotational motion has analogous concepts. Instead of force, we have torque or moment (\(M\)). Instead of linear displacement, we have angular displacement (\(\theta\)). The work done in rotational motion is done by a moment (torque) causing an angular displacement.

When a constant moment \(M\) acts on a rigid body and causes it to rotate through an angular displacement \(\theta\), the work done \(W\) by the moment is the product of the moment and the angular displacement.

The formula for work done by a constant moment is:

\[ W = M \cdot \theta \]

Here:

• \(W\) is the work done.
• \(M\) is the applied moment (or torque).
• \(\theta\) is the angular displacement (usually measured in radians).

Let's look at the given options and compare them with this fundamental formula for work done by a moment:

• Option 1: \(M\theta\)
• Option 2: \(3M\theta\)
• Option 3: \(4M\theta\)
• Option 4: \(2M\theta\)

Based on the formula for work done by a constant moment causing angular displacement, the work done is simply the product of the moment \(M\) and the angular displacement \(\theta\).

Therefore, the work done by the moment \(M\) acting on a rigid body causing an angular displacement \(\theta\) is \(M\theta\).