Units and Dimensions
Units and Dimensions: Overview
This topic covers concepts such as Dimensions, Dimensions of Fundamental Quantities, Dimensional Formula of Derived Quantities, Quantities with Same Dimensions, Dimensions of Important Quantities, and Dimensional Variables.
Important Questions on Units and Dimensions
The dimension of , where is permittivity of free space and E is electric field, is:

Which two of the following five physical parameters have the same dimensions?
(A) Energy density
(B) Refractive index
(C) Dielectric constant
(D) Young’s modulus
(E) Magnetic field

Dimensions of resistance in an electrical circuit in terms of dimension of mass , length , time and current , would be

The dimensions of Planck’s constant are same as

Which one of the following groups have quantities that do not have the same dimensions?

The dimensional formula for magnetic flux is

Which of the following will have the dimensions of time?

The dimensional formula of pressure is:

According to Newton, the viscous force acting between liquid layers of area and velocity gradient is given by Where

The dimensional formula of torque is

If and denote capacitance and resistance, the dimensional formula of is

Turpentine oil is flowing through a tube of length and radius r. The pressure difference between the two ends of the tube is p. The viscosity of oil is given by
Where is the velocity of oil at a distance from the axis of the tube. The dimensions of are:

The dimensional formula for permeability is given by

The dimensional formula for permeability is given by

The dimensional formula for angular momentum is:

What is the dimensional formula of gravitational constant?

The dimensional formula of gravitational constant is

Dimensions of coefficient of viscosity is

What is the dimensional formula of impedance?

The dimensions of torque are:
