Important questions on Dimensions And Dimensional Analysis

HARD

The potential energy of a particle varies the distance $x$ from a fixed origin as $U=x_{2}+BAx $, where A and B are dimensional constants, then find the dimensional formula for AB.

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HARD

Out of the following the only pair that does not have identical dimensions is

A

angular momentum and Planck's constant

B

moment of inertia and moment of a force

C

work and torque

D

impulse and momentum

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HARD

Find the dimensions of work.

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HARD

Find the dimensional formula for $μ_{o}$ and $ε_{o}$:

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HARD

Which of the following does not have the same dimension?

A

Electric flux, Electric field, Electric dipole moment

B

Pressure, stress, Youngs modulus

C

Electromotive force, Potential difference, Electric voltage

D

Heat, Potential energy, Work done

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HARD

Find the dimensions of refractive index.

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HARD

Two forces $P$ and $Q$ act at a point and have resultant $R$. If $Q$ is replaced by $Q(R_{2}−P_{2}) $ acting in the direction opposite to that of $Q$, the resultant:

A

remains same

B

becomes half

C

becomes twice

D

none of these

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HARD

Multiple Correct Answers Type Which of the following pairs have the same dimensions? (L = inductance, C = capacitance, R = Resistance)

This question has multiple correct options

A

$RL $ and CR

B

LR and CR

C

$RL $ and $LC $

D

RC and $LC1 $

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HARD

Planck's constant ($h$), speed of light in vacuum ($c$) and Newton's gravitational constant ($G$) are three fundamental constants. Which of the following combinations of these has the dimension of length?

A

$h_{3/2}Gc $

B

$c_{3/2}hG $

C

$c_{5/2}hG $

D

$Ghc $

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HARD

Which of the following pairs of physical quantities does not have same dimensional formula?