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Which one of the following pair has same dimensions?
1. Angular momentum and linear momentum
2. Work and power
3. Work and torque
4. Torque and pressure

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Correct Answer - Option 3 : Work and torque

Concept:

  • Dimensional Formula: It depicts the way to relate any unit to fundamental Units.
    • If we have to find The dimensional formula of any quantity, at first, we find its units in terms of these fundamental units, and then replace units with these dimensions.
  • Work: The product of force and displacement in the direction of force is called work.  Unit of work done is Joule.

1 Joule = 1 N .1 m = N m

  • Unit of force is Newton (N), the unit of distance is meter (m).
  • Torque: Torque is defined as the product of force and distance of the force from point of action
    • The unit of torque is Newton Meter N m.
  • Two physical quantities having the same units will have the same dimensions also.

Explanation:

  • Since both work and torque have the same unit, they will have the same dimensions also. 
  • The dimension of both is M L 2 T -2Work and torque have the same dimensions. 

So, the correct answer is work and torque.

  •  Angular momentum has is expressed as L = mvr, and linear momentum as p = mv. Both have different units.
  • Power is defined as rate of doing work. It is expressed as work done / time.
  • Pressure is defined as force per unit area. it is having unit, Pascal. 1 Pascal =  1 N / m2

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