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Which of the following have same dimensions

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Important Questions on Units and Measurements

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

The ratio of the dimensions of Planck’s constant to that of moment of inertia is the dimension of

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

P, Q

and

R

are physical quantities having different dimensions, which of the following combinations can never be a meaningful quantity?

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

The quantities

x = \frac{1}{\sqrt{μ_{0} \in_{0}}}, y = \frac{E}{B}

and

z = \frac{l}{C R}

are defined where C-capacitance, R-Resistance,

ℓ -

length, E-Electric field, B-magnetic field and

\in 0, μ 0, -

free space permittivity and permeability respectively. Then:

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

In the following

I

refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity:

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

A quantity

x

is given by

(\frac{I F v^{2}}{W L^{4}})

in terms of moment of inertia

I

, force

F

, velocity

v

, work

W

and length

L

. The dimensional formula for

x

is same as that of :

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Given,

B

is magnetic field induction, and

μ_{0}

is the magnetic permeability of vacuum. The dimension of

\frac{B^{2}}{2 μ_{0}}

is:

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

The dimensional formula of

\sqrt{\frac{μ_{0}}{ε_{0}}}

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Let

L, R, C

and

V

represent inductance, resistance, capacitance and voltage, respectively. The dimension of

\frac{L}{R C V}

S I

units will be:

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

A, B, C

, and

D

are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation

A D = C l n (B D)

holds true. Then which of the combination is not a meaningful quantity?

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Dimensional formula for thermal conductivity is (here

K

denotes the temperature):

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Planck's constant

(h)

, speed of light in a vacuum

(c)

and Newton's gravitational constant

(G)

are three fundamental constants. Which of the following combinations of these has the dimension of length?

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Dimensions of stress are:

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

If momentum

(P)

, area

(A)

and time

(T)

are taken to be the fundamental quantities then the dimensional formula for energy is :

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Dimension of which base quantity corresponds to that

\sqrt{\frac{G h}{c^{3}}} = ?

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

E, M, L

and

G

denote energy, mass, angular momentum and constant of gravitation respectively then

(\frac{E L^{2}}{G^{2} M^{5}})

has dimensions of

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

If $E$ and $E_{0}$ represent the energies, $t$ and $t_{0}$ represent the times, in which of the following is dimensionally correct relation?

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

The force

F

acting on a body of density

d

are related by the reflection

F = \frac{y}{\sqrt{d}}

. The dimensions of

y

are

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Time

(T)

, velocity

(C)

and angular momentum

(h)

are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be:

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Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Let $[\in_{0}]$ denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then :

Which of the following have same dimensions

Important Questions on Units and Measurements

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