In equation ∫ d t 3 a t - 2 t 2 = a x s i n - 1 t 2 a 2 - 1 , find the value of x .(Solve using dimensional analysis)

An expression which gives the relation between the derived units and fundamental units in terms of dimensions is called a dimensional equation. t 2 a 2 - 1 is dimensionless as 1 is dimentionless. So, a = t Again, 3 a t - 2 t 2 = t d t 3 a t - t 2 = t t = M 0 L 0 T 0 Thus, a x should be dimensionless, so, x = 0 .

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

The pair(s) of physical quantities that has/have the same dimensions is(are):

50% studentsanswered this correctly

Important Questions on Dimensions and Measurement

EASY

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 21

P, Q, R

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

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 22

Photon is quantum of radiation with energy

E = h ν

, where

ν

is frequency and

h

is Planck's constant. The dimensions of

h

are the same as that of

HARD

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 23

In a new hypothetical system of units, the new unit of mass is

5 kg

, new unit of length is

10 m

and new unit of time is

20 s

. Choose the correct statement(s).

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 24

If the unit of velocity is

4 m s^{- 1}

, the unit of acceleration is

24 m s^{- 2}

and the unit of force is

6 N

, then choose the correct statement(s).

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 5

Suppose two students are trying to make a new measurement system so that they can use it like a code measurement system and others do not understand it. Instead of taking $1 kg, 1 m$ and $1 s$ as basic units, they took unit of mass as $α$ $kg$ , the unit of length as $β$ $m$ and unit of time as $γ$ $s$ . They called power in the new system as $ACME$ . Then match the two columns.

	Column $A$		Column $B$
$a$	$1 N$ in new system	$p$	$α^{- 1} β^{- 2} γ^{2}$
$b$	$1 J$ in new system	$q$	$α^{- 1} β^{- 1} γ^{2}$
$c$	$1$ $Pa$ in new system	$r$	$α^{- 1} β γ^{2}$
$d$	$α$ $ACME$ in $watt$	$s$	$α^{2} β^{2} γ^{- 3}$

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 6

Match column $I$ with column $II$ and mark the correct option from the given codes. Some physical quantities are given in column $I$ and some $SI$ units in which these quantities may be expressed are given in column $II$ . Match the physical quantities in column $II$ and select the code.

	Column $I$		Column $II$
$a$	Gravitational field intensity, $I = \frac{G M_{e}}{R_{e}^{2}}$ , where $G =$ gravitational constant, $M_{e} =$ mass of the earth, $R_{e} =$ radius of the earth	$p$	$\frac{joule}{mole kelvin}$
$b$	Electric field intensity, $E = \frac{F}{Q}$ where, $F =$ force due to charge, $Q =$ electric charge	$q$	$\frac{newton}{kg}$
$c$	$R = \frac{V}{I}$ , where $V =$ potential difference across a resistance, $I =$ current in the resistance	$r$	$\frac{newton}{coulomb}$
$d$	Universal gas constant, $R = \frac{P V}{n T}$	$s$	$\frac{volt}{ampere}$

EASY

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 1

In equation

\int \frac{d t}{\sqrt{3 a t - 2 t^{2}}} = a^{x} s i n^{- 1} (\frac{t^{2}}{a^{2}} - 1)

, find the value of

x

.(Solve using dimensional analysis)

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 2

If unit of mass becomes

2

times, the unit of length becomes

4

times and the unit of time becomes

4

times in the unit of Planck's constant. Due to this, unit of Planck's constant becomes

n

times. Find the value of

n

The pair(s) of physical quantities that has/have the same dimensions is(are):

Important Questions on Dimensions and Measurement

Learn and Prepare for any exam you want !