Which two of the following five physical parameters have the same dimension?
(1) Energy density
(2) refractive index
(3) dielectric constant
(4) Young's modulus
(5) magnitic field

Options

A. (ii) and (iv)
B. (iii) and (v)
C. (i) and (iv)
D. (i) and (v)

Answer

C

Explanation

Energy density `= ("Energy")/("Volume") rArr u = (E)/(V)`
Dimensions of `u = ("Dimensions of" E)/("Dimensions of" V)`
`= ([ML^(2)T^(-2)])/([L^(3)]) = [ML^(-1)T^(-2)]`
Refractive index is a dimensionless quantity.
Dielectric constant is a dimensionless quantity.
Young's modulus `= ("Longitudinal stress")/("Longitudinal strain") = (F//A)/(Deltal//l)`
`= [ML^(-1)T^(-2)]`
Magnetic field `= ("Force")/("Charge" xx "Velcotiy") = (F)/(qv)`
`= ([MLT^(-2)])/([AT][LT^(-1)]) = [ML^(-2)A^(-1)]`