The dimension of the ratio of angular to linear momentum is

(1) ${M}^{0}{L}^{1}{T}^{0}$

(2) ${M}^{1}{L}^{1}{T}^{-1}$

(3) ${M}^{1}{L}^{2}{T}^{-1}$

(4) ${M}^{-1}{L}^{-1}{T}^{-1}$

Concept Questions :-

Dimensions
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The pair having the same dimensions is

(1) Angular momentum, work

(2) Work, torque

(3) Potential energy, linear momentum

(4) Kinetic energy, velocity

Concept Questions :-

Dimensions
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The dimensions of surface tension are

(1) $M{L}^{-1}{T}^{-2}$

(2) $ML{T}^{-2}$

(3) $M{L}^{-1}{T}^{-1}$

(4) $M{T}^{-2}$

Concept Questions :-

Dimensions
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In the following list, the only pair which have different dimensions, is

(1) Linear momentum and moment of a force

(2) Planck's constant and angular momentum

(3) Pressure and modulus of elasticity

(4) Torque and potential energy

Concept Questions :-

Dimensions
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If R and L represent respectively resistance and self inductance, which of the following combinations has the dimensions of frequency                       [ Only for droppers]

(1) $\frac{R}{L}$

(2) $\frac{L}{R}$

(3) $\sqrt{\frac{R}{L}}$

(4) $\sqrt{\frac{L}{R}}$

Concept Questions :-

Dimensions
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If velocity v, acceleration A and force F are chosen as fundamental quantities, then the dimensional formula of angular momentum in terms of v, A and F would be

(1) $F{A}^{-1}v$

(2) $F{v}^{3}{A}^{-2}$

(3) $F{v}^{2}{A}^{-1}$

(4) ${F}^{2}{v}^{2}{A}^{-1}$

Concept Questions :-

Dimensions
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The dimensions of permittivity ${\epsilon }_{0}$are

(1) ${A}^{2}{T}^{2}{M}^{-1}{L}^{-3}$

(2) ${A}^{2}{T}^{4}{M}^{-1}{L}^{-3}$

(3) ${A}^{-2}{T}^{-4}M{L}^{3}$

(4) ${A}^{2}{T}^{-4}{M}^{-1}{L}^{-3}$

Concept Questions :-

Dimensions
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Dimensions of the following three quantities are the same

(1) Work, energy, force

(2) Velocity, momentum, impulse

(3) Potential energy, kinetic energy, momentum

(4) Pressure, stress, coefficient of elasticity

Concept Questions :-

Dimensions
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The dimensions of Planck's constant and angular momentum are respectively

(1) $M{L}^{2}{T}^{-1}$ and $ML{T}^{-1}$

(2) $M{L}^{2}{T}^{-1}$ and $M{L}^{2}{T}^{-1}$

(3) $ML{T}^{-1}$ and $M{L}^{2}{T}^{-1}$

(4) $ML{T}^{-1}$ and $M{L}^{2}{T}^{-2}$

Concept Questions :-

Dimensions
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Let $\left[{\epsilon }_{0}\right]$ denotes the dimensional formula of the permittivity of the vacuum and $\left[{\mu }_{0}\right]$ that of the permeability of the vacuum. If M = mass, L = length, T = Time and I = electric current, then

(1) $\left[{\epsilon }_{0}\right]={M}^{-1}{L}^{-3}{T}^{2}I$

(2) $\left[{\epsilon }_{0}\right]={M}^{-1}{L}^{-3}{T}^{4}{I}^{2}$

(3) $\left[{\mu }_{0}\right]=ML{T}^{-2}{I}^{-3}$

(4) $\left[{\mu }_{0}\right]=M{L}^{2}{T}^{-1}I$

Concept Questions :-

Dimensions
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