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NEET PHYSICSEasy

The physical quantity that has the same dimensional formula as pressure is:

A

Force

B

Momentum

C

Young's modulus of elasticity

D

Coefficient of viscosity

Step-by-Step Solution

Let's find the dimensional formulae of the given physical quantities:

  1. Pressure: Pressure is defined as force per unit area. Dimensions of Force = [MLT2][MLT^{-2}] Dimensions of Area = [L2][L^2] Therefore, Dimensional formula of Pressure = [MLT2][L2]=[ML1T2]\frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}]

  2. Force: Its dimensional formula is [MLT2][MLT^{-2}].

  3. Momentum: It is the product of mass and velocity. Dimensional formula of Momentum = [M][LT1]=[MLT1][M][LT^{-1}] = [MLT^{-1}].

  4. Young's modulus of elasticity: It is defined as the ratio of tensile (or compressive) stress to the longitudinal strain. Stress = Force / Area, so its dimensions are same as pressure, i.e., [ML1T2][ML^{-1}T^{-2}]. Strain = Change in length / Original length, which is dimensionless [M0L0T0][M^0L^0T^0]. Therefore, Dimensional formula of Young's modulus = [ML1T2][M0L0T0]=[ML1T2]\frac{[ML^{-1}T^{-2}]}{[M^0L^0T^0]} = [ML^{-1}T^{-2}].

  5. Coefficient of viscosity: Its dimensional formula is [ML1T1][ML^{-1}T^{-1}].

From the above, we can see that the dimensional formula of Young's modulus of elasticity is the same as that of pressure.

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