The physical quantity that has the same dimensional formula as pressure is:
Force
Momentum
Young's modulus of elasticity
Coefficient of viscosity
Let's find the dimensional formulae of the given physical quantities:
Pressure: Pressure is defined as force per unit area. Dimensions of Force = Dimensions of Area = Therefore, Dimensional formula of Pressure =
Force: Its dimensional formula is .
Momentum: It is the product of mass and velocity. Dimensional formula of Momentum = .
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., . Strain = Change in length / Original length, which is dimensionless . Therefore, Dimensional formula of Young's modulus = .
Coefficient of viscosity: Its dimensional formula is .
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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