Question

Which of the following physical quantities has neither dimensions nor unit?

• A. Angle
• B. Luminous intensity
• C. Coefficient of friction
• D. Current

Answer 1

Answer: (C)

Unit less physical quantities are always dimensionless. For example, refractive index and relative density. These quantities are the ratio of same physical quantities.
A dimensionless physical quantity may have a unit. For example, plane angle and solid angle. The unit of plane angle is radian but it is dimensionless.
Now,
$\text{Coefficient of friction}=\frac{\text{friction force}}{\text{Normal reactiom}}$
$=\frac{\left[{\text{MLT}}^{-2}\right]}{\left[{\text{MLT}}^{-2}\right]}$ = no dimensions
Unit= $\frac{\text{N}}{\text{N}}$ = no unit
The coefficient of friction is the ratio of two forces. Hence, it is dimensionless. It also don't have any unit.