Question

Which of the following physical quantity has the dimensional formula of M¹L^-1T^-2 ?
1. Force
2. Acceleration 
3. Pressure
4. Density

Answer 1

Correct Answer - Option 3 : Pressure

CONCEPT:

• The dimension of a physical quantity: It is the power to which the fundamental units must be raised to represent the physical quantity.
  • For example; The dimension of mass is [M1L0T0] and that of length is [M0L1T0].

• Pressure(P): The force (F) per unit area (A) is called pressure.

​P = F/A

Acceleration (a) = (v- u)/t 

Where v and u are final and initial velocities respectively that have the dimension [M0L1T-1] and t = time that has dimension [M0L0T1].

It multiplies to give a dimensional formula of [M0L1T-2].

Force (F) = ma 

The mass and acceleration have the dimensions of [M1L0T0] and [M0L1T-2] respectively, it multiplies to give the dimension of [M1L1T-2].

• Hence, the force has the dimensions of [M1L1T-2].

EXPLANATION:

Pressure (P) = F/A

F = force that has the dimension of [M1L1T-2] and A = area that has the dimension of [M0L2T0].

Dimensions of P = [F]/[A] = [M1L-1T-2].