Question

Which of the following is dimensionless?

• A. Universal gravitational constant
• B. Relative permittivity
• C. Relative velocity
• D. Plancks constant

Answer 1

Answer: (B)

The ratio of permittivity of free space $\left({\epsilon }_0\right)$ and permittivity of medium $(\epsilon )$ is called the dielectric constant $K$,
or relative permittivity of the medium $K=\frac{\epsilon }{{\epsilon }_0}$
Hence, it is dimensionless.
Whereas dimensions of universal gravitational constant $(G)$ are $\left[M^{-1}{L}^3{T}^{-2}\right]$, Relative velocity $\left[L{T}^{-1}\right]$, and Plancks constant has dimensions $\left[M{L}^2{T}^{-1}\right]$.