Units and Dimensions

IMPORTANT

Units and Dimensions: Overview

This topic covers concepts such as Dimensions, Dimensions of Fundamental Quantities, Dimensional Formula of Derived Quantities, Quantities with Same Dimensions, Dimensions of Important Quantities, and Dimensional Variables.

Important Questions on Units and Dimensions

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IMPORTANT

The dimension of 1 2 ε 0 E 2 , where   ε 0 is permittivity of free space and E is electric field, is:

MEDIUM
IMPORTANT

Which two of the following five physical parameters have the same dimensions?
(A) Energy density
(B) Refractive index
(C) Dielectric constant
(D) Young’s modulus
(E) Magnetic field

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Dimensions of resistance in an electrical circuit in terms of dimension of mass M, length L, time T and current I, would be

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The dimensions of Planck’s constant are same as

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Which one of the following groups have quantities that do not have the same dimensions?

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The dimensional formula for magnetic flux is

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Which of the following will have the dimensions of time?

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The dimensional formula of pressure is:

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According to Newton, the viscous force acting between liquid layers of area A and velocity gradient  ΔvΔz is given by F=-ηAΔvΔz Where η is the constant, called coefficient of viscosity. The dimensional formula of η is

EASY
IMPORTANT

The dimensional formula of torque is

EASY
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If C and R denote capacitance and resistance, the dimensional formula of CR is

MEDIUM
IMPORTANT

Turpentine oil is flowing through a tube of length l and radius r. The pressure difference between the two ends of the tube is p. The viscosity of oil is given by

                          η= p( r 2 x 2 ) 4vl

Where v is the velocity of oil at a distance x from the axis of the tube. The dimensions of   η are:

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The dimensional formula for permeability μ is given by

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The dimensional formula for permeability μ is given by

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The dimensional formula for angular momentum is:

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What is the dimensional formula of gravitational constant?

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The dimensional formula of gravitational constant is

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Dimensions of coefficient of viscosity is

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What is the dimensional formula of impedance?

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The dimensions of torque are: