Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R) Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension S , if density of the liquid is ρ and radius of the drop is r , then T = K ρ r 3 S 3 2 is dimensionally correct, where K is dimensionless. Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period. In the light of above statements, choose the correct answer from the options given below.

Both (A) and (R) are true and (R) is the correct explanation of (A)

Both (A) and (R) are true but (R) is not the correct explanation of (A)

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JEE Main

IMPORTANT

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In a Vernier Caliper $10$ divisions of Vernier scale is equal to the $9$ divisions of main scale. When both jaws of Vernier Calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and $4^{th}$ Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to $1 mm$ . While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between $30$ and $31$ divisions of main scale reading and $6^{th}$ Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be:

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Important Questions on Physics and Measurement

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 27 July 2022 Shift 1>Q 106

A torque meter is calibrated to reference standards of mass, length and time each with

5 %

accuracy. After calibration, the measured torque with this torque meter will have net accuracy of

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 27 July 2022 Shift 1>Q 107

The one division of main scale of vernier callipers reads

1 mm

and

10

divisions of Vernier scale is equal to the

9

divisions on main scale. When the two jaws of the instrument touch each other the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between

4.1 cm

and

4.2 cm

and

6^{th}

Vernier division coincides with a main scale division. The diameter of the bob will be _____

10^{- 2} cm

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 27 July 2022 Shift 2>Q 108

An expression of energy density is given by

u = \frac{α}{β} \sin (\frac{α x}{k t})

, where

α, β

are constants,

x

is displacement,

k

is Boltzmann constant and

t

is the temperature. The dimensions of

β

will be

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 28 July 2022 Shift 1>Q 109

The dimensions of $(\frac{B^{2}}{μ_{0}})$ will be

(if $μ_{0}$ : permeability of free space and $B :$ magnetic field)

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 28 July 2022 Shift 2>Q 110

Consider the efficiency of Carnot's engine is given by

η = \frac{α β}{\sin θ} \log_{e} \frac{β x}{k T}

, where

α

and

β

are constants. If

T

is temperature,

k

is Boltzman constant,

θ

is angular displacement and

x

has the dimensions of length. Then, choose the incorrect option.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 28 July 2022 Shift 2>Q 111

In an experiment to find acceleration due to gravity

(g)

using simple pendulum, time period of

0.5 s

is measured from time of

100

oscillation with a watch of

1 s

resolution. If measured value of length is

10 cm

known to

1 mm

accuracy. The accuracy in the determination of

g

is found to be

x %

. The value of

x

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 1 - Physics and Measurement>JEE Main - 29 July 2022 Shift 1>Q 112

Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R)

Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension $(S)$ , if density of the liquid is $ρ$ and radius of the drop is $r$ , then $T = K \sqrt{\frac{ρ r^{3}}{S^{\frac{3}{2}}}}$ is dimensionally correct, where $K$ is dimensionless.

Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period. In the light of above statements, 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 - 29 July 2022 Shift 1>Q 113

A travelling microscope has

20

divisions per

cm

on the main scale while its Vernier scale has total

50

divisions and

25

Vernier scale divisions are equal to

24

main scale divisions, what is the least count of the travelling microscope ?

Important Questions on Physics and Measurement

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