# What is the dimensional formula of Work? (a) ML2T-2 (b) ML-1T-3 (c) MLT3 (d) ML-1T-2

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The dimensional formula of Work is ML2T-2. Work done is the dot product of displacement and force. Joules are the Work SI unit. Work done is written as,

Work done (W) = F.s cos θ _____(1)

Where,

• F = force
• s = displacement
• θ = angle between F and s.

### Dimensional Formula of Work

We know that: Work done (W) = F.s cos θ _____(1)

Force = mass × acceleration

Dimensional formula of force

F = [MLT-2]

Dimensional formula of displacement

s = [L]

From equation (1), enter the force and displacement numbers without considering the angle.

Work done W = F.s

= MLT-2.L

= ML2T-2

Hence, the dimensional formula of work (W) = [ML2T-2]

Factors Affecting Work:

Force:

Any mass-containing object that experiences force will alter in acceleration and velocity. The amount and direction of force are both characteristics of a vector quantity. No work is done by force if the force acting on an object is zero, regardless of whether the item is in a dynamic or static state

Displacement:

The vector variable known as displacement provides the shortest distance between any object’s starting and ending positions. The network that a force does on an object is zero if the resultant displacement in the direction of the force caused by a force acting on that object is zero. For instance, if we use all of our force against a stiff wall and still cannot move it, we can conclude that no work has been done on the wall.

Summary:

## What is the dimensional formula of Work? (a) ML2T-2 (b) ML-1T-3 (c) MLT3 (d) ML-1T-2

The dimensional formula of Work is ML2T-2. Force and displacement are multiplied together to create work.

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