Answer:

To determine the dimensions of the expression EM QB^2, we can break it down into its constituent parts and analyze the dimensions of each component.

Electric Field (E):
The electric field is a measure of the force exerted on a charged particle in an electric field. Its dimensions can be determined using Coulomb's law, which states that the electric field is equal to the force experienced by a charged particle (F) divided by the charge (Q) of the particle. Therefore, the dimensions of the electric field can be expressed as [E] = [F]/[Q].

Magnetic Field (B):
The magnetic field is a measure of the magnetic force experienced by a moving charged particle. Its dimensions can be determined using the equation for the magnetic force (F) on a charged particle, which is given by the product of the magnetic field (B), the charge (Q), and the velocity (v) of the particle. Therefore, the dimensions of the magnetic field can be expressed as [B] = [F]/[Q][v].

Mass (M):
Mass is the measure of the amount of matter in an object. Its dimensions are typically expressed as [M].

Charge (Q):
Charge is a fundamental property of matter and can be positive or negative. Its dimensions are typically expressed as [Q].

Dimensions of EM QB^2:
Using the dimensions of electric field ([E]), magnetic field ([B]), mass ([M]), and charge ([Q]), we can determine the dimensions of the expression EM QB^2.

The expression EM QB^2 can be written as [E][M][Q][B^2]. By substituting the dimensions of each component, we can determine the overall dimensions:

[E][M][Q][B^2] = ([F]/[Q])[M][Q][F^2]/[Q^2][v^2]

Simplifying the expression, we get:

[E][M][Q][B^2] = [F]^3/[v^2]

Therefore, the dimensions of EM QB^2 are given by [F]^3/[v^2].

Answer: (d) None of these