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 $\left(\varepsilon_{0}\right)$ and permittivity of medium $(\varepsilon)$ is called the dielectric constant $K$,
or relative permittivity of the medium $K=\frac{\varepsilon}{\varepsilon_{0}}$
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 $\left[M L^{2} T^{-1}\right]$.