EASY

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Obtain an expression for the centripetal force $F$ acting on a particle of mass $m$ moving with velocity $v$ in a circle of radius $r$ . Take dimensionless constant $K = 1$

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Important Questions on Units and Measurements

EASY

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

A quantity

f

is given by

f = \sqrt{\frac{h c^{5}}{G}}

where

c

is speed of light,

G

universal gravitational constant and

h

is the Planck’s constant. Dimension of

f

is that of:

MEDIUM

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

S I

units, the dimensions of

\sqrt{\frac{ϵ_{0}}{μ_{0}}}

is:

EASY

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

EASY

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?

HARD

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

The dimensions of the area A of a black hole can be written in terms of the universal gravitational constant G, its mass M and the speed of light c as

A = G^{α} M^{β} c^{7} .

Here-

EASY

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:

MEDIUM

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

Which of the following combinations has the dimension of electrical resistance

(ϵ_{0}

is the permittivity of vacuum and

μ_{0}

is the permeability of vacuum)?

EASY

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 :

MEDIUM

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

The dimensions of Stefan-Boltzmann constant

σ

can be written in terms of Planck's constant

h

, Boltzmann constant

k_{B}

and the speed of light c as

σ = h^{α} {(k_{B})}^{β} c^{γ}

. Here

EASY

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:

EASY

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:

EASY

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?

MEDIUM

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

If speed

V

, area

A

and force

F

are chosen as fundamental units, then the dimension of Young's modulus will be :

EASY

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:

EASY

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 :

EASY

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

Dimensional formula for thermal conductivity is (here

K

denotes the temperature):

EASY

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:

MEDIUM

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

If Surface tension

(S)

, Moment of Inertia

(I)

and Planck's constant

(h),

were to be taken as the fundamental units, the dimensional formula for linear momentum would be:

MEDIUM

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

Stoke's law states that the viscous drag force $F$ experienced by a sphere of radius $a$ a, moving with a speed $v$ through a fluid with coefficient of viscosity $η$ , is given by $F = 6 π η a v$ .

If this fluid is flowing through a cylindrical pipe of radius $r$ , length $l$ and a pressure difference of $P$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as, $\frac{V}{t} = k {(\frac{P}{l})}^{a} η^{b} r^{c}$ , where $k$ is a dimensionless constant. Correct values of $a, b$ and $c$ are-

MEDIUM

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

If electronic charge

e

, electron mass

m

, speed of light in vacuum

c

and Planck's constant

h

are taken as fundamental quantities, the permeability of vacuum

μ_{0}

can be expressed in units of:

Obtain an expression for the centripetal force F acting on a particle of mass m moving with velocity v in a circle of radius r. Take dimensionless constant K=1

Important Questions on Units and Measurements

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Obtain an expression for the centripetal force $F$ acting on a particle of mass $m$ moving with velocity $v$ in a circle of radius $r$ . Take dimensionless constant $K = 1$