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NEET
Exam
NEET
Subject
Physics
Chapter
Units and Dimensions

NEET · Physics · Units and Dimensions

Which of the following physical quantities has the same dimensional...

Which of the following physical quantities has the same dimensional formula as the expression B22μ0\dfrac{B^2}{2\mu_0}, where BB is the magnetic field and μ0\mu_0 is the permeability of free space?

Options

  1. AForce
  2. BPower
  3. CPressure
  4. DEnergy

Correct answer

C. Pressure

Step-by-step solution

The expression B22μ0\dfrac{B^2}{2\mu_0} represents the magnetic energy density, which is the magnetic energy stored per unit volume.

Dimensional formula of energy =[ML2T−2]= [ML^2T^{-2}]
Dimensional formula of volume =[L3]= [L^3]

Dimensional formula of energy density =[ML2T−2][L3]=[ML−1T−2]= \dfrac{[ML^2T^{-2}]}{[L^3]} = [ML^{-1}T^{-2}]

Now, let us check the dimensions of the given options:
(1) Force =[MLT−2]= [MLT^{-2}]
(2) Power =[ML2T−3]= [ML^2T^{-3}]
(3) Pressure =ForceArea=[MLT−2][L2]=[ML−1T−2]= \dfrac{\text{Force}}{\text{Area}} = \dfrac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}]
(4) Energy =[ML2T−2]= [ML^2T^{-2}]

Thus, the expression has the same dimensions as pressure.

Answer: Pressure
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