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NEET
Exam
NEET
Subject
Physics
Chapter
Units and Dimensions

NEET · Physics · Units and Dimensions

Given below are two statements: one is labelled as Assertion (A)...

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): Pressure and energy density have the same dimensional formula.
Reason (R): Energy density is defined as the force acting per unit area.

In the light of the above statements, choose the most appropriate answer from the options given below.

Options

  1. ABoth Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  2. BAssertion (A) is true but Reason (R) is false.
  3. CBoth Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
  4. DAssertion (A) is false but Reason (R) is true.

Correct answer

B. Assertion (A) is true but Reason (R) is false.

Step-by-step solution

Assertion (A) is true: The dimensional formula of pressure is P=ForceArea=[MLT−2][L2]=[ML−1T−2]P = \dfrac{\text{Force}}{\text{Area}} = \dfrac{[\text{MLT}^{-2}]}{[\text{L}^2]} = [\text{ML}^{-1}\text{T}^{-2}].
Energy density is energy per unit volume, so its dimensional formula is u=EnergyVolume=[ML2T−2][L3]=[ML−1T−2]u = \dfrac{\text{Energy}}{\text{Volume}} = \dfrac{[\text{ML}^2\text{T}^{-2}]}{[\text{L}^3]} = [\text{ML}^{-1}\text{T}^{-2}].
Thus, pressure and energy density have the same dimensional formula.

Reason (R) is false: Energy density is defined as the energy stored per unit volume, not as force acting per unit area (which is the definition of pressure). Although they are dimensionally equivalent, their physical definitions are entirely different.

Answer: Assertion (A) is true but Reason (R) is false.
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