Match List - I with List - II : List - I List - II a h (Planck's constant) i MLT - 1 b E (kinetic energy) ii ML 2 T - 1 c V (electric potential) iii ML 2 T - 2 d P (linear momentum) iv ML 2 I - 1 T - 3 Choose the correct answer from the options given below:

a → ii , b → iii , c → iv , d → i

a → i , b → ii , c → iv , d → iii

a → iii , b → ii , c → iv , d → i

a → iii , b → iv , c → ii , d → i

EASY

JEE Main

IMPORTANT

Earn 100

The work done by a gas molecule in an isolated system is given by, $W = α β^{2} e^{- \frac{x^{2}}{α k T}},$ where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature. $α$ and $β$ are constants. Then the dimensions of $β$ will be:

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Important Questions on Physics and Measurement

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 24 Feb 2021 Shift 2>Q 29

The period of oscillation of a simple pendulum is

T = 2 π \sqrt{\frac{L}{g}} .

Measured value of

L

1.0 m

from meter scale having a minimum division of

1 mm

and time of one complete oscillation is

1.95 s

measured from stopwatch of

0.01 s

resolution. The percentage error in the determination of

' g'

will be:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 25 Feb 2021 Shift 1>Q 30

The pitch of the screw gauge is

1 mm

and there are

100

divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies

8

divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while

72^{nd}

division on circular scale coincides with the reference line. The radius of the wire is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 25 Feb 2021 Shift 1>Q 31

Match List - I with List - II :

	$List - I$		$List - II$
$(a)$	$h$ (Planck's constant)	$(i)$	$[{MLT}^{- 1}]$
$(b)$	$E$ (kinetic energy)	$(ii)$	$[{ML}^{2} T^{- 1}]$
$(c)$	$V$ (electric potential)	$(iii)$	$[{ML}^{2} T^{- 2}]$
$(d)$	$P$ (linear momentum)	$(iv)$	$[{ML}^{2} I^{- 1} T^{- 3}]$

Choose the correct answer from the options given below:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 25 Feb 2021 Shift 2>Q 32

e

is the electronic charge,

c

is the speed of light in free space and

h

is Planck's constant, the quantity

\frac{1}{4 π ε_{0}} \frac{{|e|}^{2}}{h c}

has dimensions of :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 26 Feb 2021 Shift 1>Q 33

In a typical combustion engine the workdone by a gas molecule is given by

W = α^{2} β e^{\frac{- β x^{2}}{k T}}

, where

x

is the displacement,

k

is the Boltzmann constant and

T

is the temperature. If

α

and

β

are constants, dimensions of

α

will be:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 26 Feb 2021 Shift 2>Q 34

C

and

V

represent capacity and voltage respectively then what are the dimensions of

λ

where

C / V = λ

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 2 September 2020 Shift 1>Q 35

The least count of the main scale of a vernier calipers is

1 mm

. Its vernier scale is divided into

10

divisions and coincide with

9

divisions of the main scale. When jaws are touching each other, the

7^{th}

division of the vernier scale coincides with a division of the main scale and the zero of vernier scale is lying right side of the zero of the main scale. When this vernier is used to measure the length of the cylinder the zero of the vernier scale between

3.1 cm

and

3.2 cm

and

4^{th}

VSD coincides with the main scale division. The length of the cylinder is (VSD is vernier scale division)

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 2 September 2020 Shift 1>Q 36

If speed

V

, area

A

and force

F

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

The work done by a gas molecule in an isolated system is given by, W=αβ2e-x2αk T, where x is the displacement, k is the Boltzmann constant and T is the temperature. α and β are constants. Then the dimensions of β will be:

Important Questions on Physics and Measurement

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The work done by a gas molecule in an isolated system is given by, $W = α β^{2} e^{- \frac{x^{2}}{α k T}},$ where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature. $α$ and $β$ are constants. Then the dimensions of $β$ will be: