Which two of the following five physical paramenters have the same dimensions?
(i) Energy density
(ii) Refractive index
(iii) Dielectric constant
(iv) Young's modulus
(v) Magnetic field

Options

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

Answer

A

Explanation

Energy density = `("Energy")/("volume") = ([M^(1)L^(2)T^(-2)])/([L^(3)])`
`" "= [M^(1)L^(-1)T^(-2)]`
refractive index = dimensionless
dielectric constant = dimension less
young modulus `= ("stress")/("strain") = [M^(1)L^(-1)T^(-2)]`
Magnetic field = `("force")/("pole strength")= ([M^(1)L^(1)T^(-2)])/([AL])`
`" " = [M^(1)T^(-2)A^(-1)]`
(a, d) and (b, c) having same dimensions