Which of the following two parameter have same dimension?
(a) energy density (b) refractive index
(c) dielectric constant (d) Young's modulus
(e) electric field.

Options

A. (b) and (d)
B. (c) and (e)
C. (a) and (d)
D. (a) and (e)

Explanation

[Energy density]`=(["Energy"])/(["Volume"])`
`=(ML^(2)T^(-2))/(L^(3)) =ML^(-1)T^(-2)`
[Refractive index] `([c])/([v])`
`=(LT^(-1))/(LT^(-1))=M^(0)L^(0)T^(0)`
where c= speed of ligth in vaccum
v= speed of light in medium
[dielectric constant] `=([E])/([E_(0)])=M^(0)L^(0)T^(0)`
where E and `E_(0)` are permittivity in medium and vaccum.
[Young.s modulus] `=("Stress")/("Strain")`
`=([F][l])/([A][Deltal])`
`=((MLT^(-2))(L))/((L^(2))(L))`
`=ML^(-1)T^(-2)`
[Magnetic field `(B)=(F)/(I l sin theta)[ L, F= BI l sin theta]`
`sin theta` is dimensionless.
`[B]=([F])/([I][l][sin theta])`
`=(MLT^(-2))/((A)(L)(M^(0)L^(0)T^(0))`
`:.` Option (C) is correct