Velocity v and acceleration a in two systems of units 1 and 2 are related as v 2 = n m 2 v 1 and a 2 = a 1 m n respectively. Here m and n are constants. The relations for distance and time in two systems respectively are

n 3 m 3 L 1 = L 2 and n 2 m T 1 = T 2

L 1 = n 4 m 2 L 2 and T 1 = n 2 m T 2

L 1 = n 2 m L 2 and T 1 = n 4 m 2 T 2

n 2 m L 1 = L 2 and n 4 m 2 T 1 = T 2

Match the physical quantities with their correct SI units. List-I List-II (A) Planck's constant (I) kg m s - 2 (B) Torque (II) kg - 1 m 3 (C) Weight (III) m 2 kg s - 1 (D) Specific volume (IV) kg m 2 s - 2 The correct match is

A = III , B = IV , C = I , D = II

A = II , B = IV , C = I , D = III

A = IV , B = I , C = II , D = III

A = II , B = III , C = I , D = IV

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In SI units, $kg m^{2} s^{- 2}$ is equivalent to which of the following?

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Important Questions on Units and Measurements

EASY

Physics>Mechanics>Units and Measurements>The International System of Units

Plane angle and solid angle have:

EASY

Physics>Mechanics>Units and Measurements>The International System of Units

Light year is a unit of

MEDIUM

Physics>Mechanics>Units and Measurements>The International System of Units

Velocity

(v)

and acceleration

(a)

in two systems of units

1

and

2

are related as

v_{2} = \frac{n}{m^{2}} v_{1}

and

a_{2} = \frac{a_{1}}{m n}

respectively. Here

m

and

n

are constants. The relations for distance and time in two systems respectively are

EASY

Physics>Mechanics>Units and Measurements>The International System of Units

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>The International System of Units

The prefix atto means

MEDIUM

Physics>Mechanics>Units and Measurements>The International System of Units

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>The International System of Units

The distance of the Sun from earth is

1.5 \times 10^{11} m

and its angular diameter is

2000''

when observed from the earth. The diameter of the Sun will be

MEDIUM

Physics>Mechanics>Units and Measurements>The International System of Units

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:

EASY

Physics>Mechanics>Units and Measurements>The International System of Units

If $E$ and $H$ represents the intensity of electric field and magnetizing field respectively, then the unit of $\frac{E}{H}$ will be:

MEDIUM

Physics>Mechanics>Units and Measurements>The International System of Units

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>The International System of Units

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>The International System of Units

Match the physical quantities with their correct $SI$ units.

	List-I		List-II
(A)	Planck's constant	(I)	$kg m s^{- 2}$
(B)	Torque	(II)	${kg}^{- 1} m^{3}$
(C)	Weight	(III)	$m^{2} kg s^{- 1}$
(D)	Specific volume	(IV)	$kg m^{2} s^{- 2}$

The correct match is

MEDIUM

Physics>Mechanics>Units and Measurements>The International System of Units

Expression for time in terms of

G

(universal gravitational constant),

h

(Planck constant) and

c

(speed of light) is proportional to:

EASY

Physics>Mechanics>Units and Measurements>The International System of Units

Match List I with List II

	List I		List II
A	Torque	I	$kg m^{- 1} s^{- 2}$
B	Energy density	II	$kg m s^{- 1}$
C	Pressure gradient	III	$kg m^{- 2} s^{- 2}$
D	Impulse	IV	$kg m^{2} s^{- 2}$

Choose the correct answer from the options given below :

EASY

Physics>Mechanics>Units and Measurements>The International System of Units

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>The International System of Units

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?

HARD

Physics>Mechanics>Units and Measurements>The International System of Units

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)

EASY

Physics>Mechanics>Units and Measurements>The International System of Units

The angular speed of a fly-wheel making

180 rpm

is ________

EASY

Physics>Mechanics>Units and Measurements>The International System of Units

Pick out the stranger

EASY

Physics>Mechanics>Units and Measurements>The International System of Units

The angle of

1'

(minute of arc) in radian is nearly equal to

In SI units, kg m2 s-2 is equivalent to which of the following?

Important Questions on Units and Measurements

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In SI units, $kg m^{2} s^{- 2}$ is equivalent to which of the following?