Question

Which of the following physical quantities have the same dimensions?
(1) Energy density (2) Refractive index
(3) Magnetic induction (4) Pressure
A. 1 and 2
B. 2 and 3
C. 1 and 4
D. 1 and 3

Answer 1

Correct Answer - c
(1) Energy density = `[("Energy")/("Volume")]`
`[(L^(2)M^(1)T^(-2))/(L^(3))]`
`=[L^(-1)M^(1)T^(-2)]`
(2) Refractive index has no dimensions.
(3) Magnetic induction (B) `because F=BIl`
`therefore [B]=[(F)/(Il)]=[(M^(1)L^(1)T^(-2))/(A^(1)L^(1))]=[M^(1)A^(-1)T^(-2)]`

(4) `therefore` [Pressure] `=[(F)/(A)]=[(L^(1)M^(1)T^(-2))/(L^(2))]`
`=[L^(-1)M^(1)T^(-2)]`
Thus (1) and (4) have the same dimensions.