Question

Which two of the following five physical parameters have the same dimensions ?
(a) energy density (b) refractive index
(c) dielectric constant (d) Young's modulus
(e) magnetic field
(1) (a), (d)
(2) (a), (e)
(3) (b), (d)
(4) (c), (e)​

Answer 1

Answer:

Option A is the correct answer

Explanation:

(a) For Energy Density-:

$\bold{Energy \: Density} = \frac{Energy }{Volume} \\ \bold{Energy \: Density} = \frac{ {M}^{1} {L}^{2} {T}^{ - 2} }{ {L}^{3} } \\ \bold{Energy \: Density} = [ {M}^{1} {L}^{ - 2} {T}^{ - 2} ]$

We know that -:

(b) Refractive Index = Dimensionless

(c) Dielectric constant = Dimension less

(d) For Young Modulus-:

$\bold{Young \: Modulus} = \frac{Stress}{Strain} \\ \bold{Young \: Modulus} = [ {M}^{1} {L}^{ - 1} {T}^{ - 2} ]$

(e) For Magnetic Field-:

$\bold{Magnetic \: Field } = \frac{Force}{Pole \: Strength} \\ \bold{Magnetic \: Field } = \frac{ {M}^{1} {L}^{2} {T}^{ - 2} }{AL} \\ \bold{Magnetic \: Field } = [ {M}^{1} {T}^{ - 2} {A}^{ - 1} ]$

From Calculation-:

(a,d) and (b,c) is having same dimensions.

Answer 2

Answer:

option A is the correct answer