Dimensional Analysis of Physical Quantities mcq Test

We know that angle is dimensionless quantity and it is measured in radians. Therefore a dimensionless quantity may have a unit.

We know that the angle, strain and specific gravity are the ratios of fundamental units. Therefore all of those are dimensionless quantities.

We know that the angular velocity = [Angle/ Time]
Therefore dimensional formula of angular velocity = [Dimensions of angle / Dimensions of time]
= [M⁰L⁰T⁰] / [M⁰L⁰T] = [M⁰L⁰T^-1]

We know that impulse = Force × Time.
Therefore dimensions of impulse = Dimensions of force × Dimensions of time
= [MLT^-2] [M⁰L⁰T] = [MLT^-1]

We know that the coefficient of friction (µ) = [Frictional force / Normal reaction].
Therefore dimensions of coefficient of friction = [Dimension of force / Dimension of reaction]
= [MLT^-2] / [MLT^-2] = [M⁰LT⁰]

We know that the energy of a body is the capacity to do some work in joules.
Therefore dimensions of energy will be same as that of work/
Therefore dimensions of work = Dimensions of force × Dimensions of distance
= [MLT^-2] [M⁰LT⁰] = [ML²T^-2]

We know that power (P) = [Work / Time]
Therefore dimensions of the power = [Dimensions of work / Dimensions of time] [ML²T^-2] / [M⁰L⁰T]
= [ML²T^-3]

We know that angular momentum = Mass × Angular velocity × Radius.
Therefore dimensional formula for angular momentum
= Dimensions of mass × Dimensions of velocity × Dimensions of radius
= [ML⁰T⁰] [M⁰LT^-1] [M⁰LT⁰] = [ML²T^-1]

We know that torque (τ) = Force × Distance
Therefore dimensions of torque
= Dimensions of force × Dimensions of distance
= [MLT^-2] [M⁰LT⁰] = [ML²T^-2]

We know that gravitational constant (G)
= [Force × (Distance)²] / (Mass)²
= [Dimensions of Force × (Dimensions of Distance)²] / (Dimensions of Mass)²
= [MLT^-2] [M⁰LT⁰]² / [ML⁰T⁰]² = [M^-1L³T^-2]

We know that Young’s modulus (Y) = Stress / Strain.
Therefore dimensional representation of Young’s modulus (Y)
= Dimensions of stress / Dimensions of strain
= [ML^-1T^-2] / [M⁰L⁰T⁰]
= [ML^-1T^-2]

We know that strain = Change in length / Original length
since both the denominator and numerator have the same dimensions, i.e. [M⁰L⁰T⁰], Therefore strain is a dimensionless quantity.

We know that strain = Change in length / Original length
Therefore dimensions of strain            = Dimensions of change in length / Dimensions of original length
= [M⁰LT⁰] / [M⁰LT⁰] = [M⁰L⁰T⁰]
Therefore strain is a dimensionless quantity.

We know that angle of contact is an angle which is a dimensionless quantity. Therefore dimensional formula for angle of contact = [M⁰L⁰T⁰]

We know that relative density (ρ_r) = Density of substance / Density of water at 4℃
Since both the denominator and numerator has the dimensions of density i.e., [ML^-3T⁰]
therefore dimensional formula of relative density = [M⁰L⁰T⁰]