EASY

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Time is an example of fundamental quantities.

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Important Questions on Units and Measurements

MEDIUM

Physics>Mechanics>Units and Measurements>Physical Quantities

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:

MEDIUM

Physics>Mechanics>Units and Measurements>Physical Quantities

The density of a material in

SI

units is

128 kg m^{- 3} .

In certain units in which the unit of length is

25 cm

and the unit of mass is

50 g,

the numerical value of density of the material is:

EASY

Physics>Mechanics>Units and Measurements>Physical Quantities

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

EASY

Physics>Mechanics>Units and Measurements>Physical Quantities

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>Physical Quantities

Consider a particle moving along the positive direction of

X

-axis. The velocity of the particle is given by

v = α \sqrt{x}

(

α

is a positive constant). At time

t = 0

, if the particle is located at

x = 0

, the time dependence of the velocity and the acceleration of the particle are respectively.

HARD

Physics>Mechanics>Units and Measurements>Physical Quantities

If energy

(E)

, velocity

(V)

and time

(T)

are chosen as the fundamental quantities, the dimensional formula of surface tension will be___(For surface tension, Force=Surface tension

\times

length)

MEDIUM

Physics>Mechanics>Units and Measurements>Physical Quantities

Expression for time in terms of

G

(universal gravitational constant),

h

(Planck constant) and

c

(speed of light) is proportional to:

HARD

Physics>Mechanics>Units and Measurements>Physical Quantities

In terms of potential difference

V

, electic current

I

, permittivity

ε_{0}

, permeability

μ_{0}

and speed of light

c

, the dimensionally correct equation(s) is (are)

MEDIUM

Physics>Mechanics>Units and Measurements>Physical Quantities

A length - scale

(l)

depends on the permittivity

(ε)

of a dielectric material, Boltzmann constant

k_{B}

, the absolute temperature T, the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles, Which of the following expressions (s) for

l

is (are) dimensionally correct?

EASY

Physics>Mechanics>Units and Measurements>Physical Quantities

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>Physical Quantities

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:

MEDIUM

Physics>Mechanics>Units and Measurements>Physical Quantities

A huge circular arc of length $4.4 ly$ subtends an angle $4 s$ at the centre of the circle. How long it would take for a body to complete $4$ revolution if its speed is $8 AU$ per second?
Given : $1 ly = 9.46 \times 10^{15} m$

$1 AU = 1.5 \times 10^{11} m$

MEDIUM

Physics>Mechanics>Units and Measurements>Physical Quantities

A physical quantity of the dimensions of length that can be formed out of

c, G

and

\frac{e^{2}}{4 π ε_{0}}

, where [

c

is velocity of light,

G

is universal constant of gravitation,

e

is charge &

ε_{0}

is permittivity of free space]:

MEDIUM

Physics>Mechanics>Units and Measurements>Physical Quantities

A beaker contains a fluid of density

ρ

\frac{k g}{m^{3}}

, specific heat

S \frac{J}{k g^{o} C}

and viscosity

η

. The beaker is filled up to height h. To estimate the rate of heat transfer per unit area

(\frac{\dot{Q}}{A})

by convection when beaker is put on a hot plate, a student proposes that it should depend on

η

(\frac{S Δ θ}{h})

and

(\frac{1}{ρ g})

when

Δ θ

(

{i n}^{o} C

) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for

(\frac{\dot{Q}}{A})

is:

HARD

Physics>Mechanics>Units and Measurements>Physical Quantities

Planck' constant

h

, speed of light

c

and gravitational constant

G

are used to form a unit of length

L

and a unit of mass

M

. Then the correct option(s) is (are)

EASY

Physics>Mechanics>Units and Measurements>Physical Quantities

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?

EASY

Physics>Mechanics>Units and Measurements>Physical Quantities

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:

MEDIUM

Physics>Mechanics>Units and Measurements>Physical Quantities

The least count of the main scale of a screw gauge is

1 mm .

The minimum number of divisions on its circular scale required to measure

5 μm

diameter of a wire is:

MEDIUM

Physics>Mechanics>Units and Measurements>Physical Quantities

For the four sets of three measured physical quantities as given below. Which of the following options is correct?

(i)

A_{1} = 24.36, B_{1} = 0.0724, C_{1} = 256.2

(i i)

A_{2} = 24.44, B_{2} = 16.082, C_{2} = 240.2

(i i i)

A_{3} = 25.2, B_{3} = 19.2812, C_{3} = 236.183

(i v)

A_{4} = 25, B_{4} = 236.191, C_{4} = 19.5

EASY

Physics>Mechanics>Units and Measurements>Physical Quantities

The angle of

1'

(minute of arc) in radian is nearly equal to

Time is an example of fundamental quantities.

Important Questions on Units and Measurements

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