Core Syllabus Module

Physics and Measurement

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JEE Advanced 2025

LEVELJEE Advanced

A single slit diffraction experiment is performed to determine the slit width using the equation, $\frac{b d}{D} = mλ$ , where $b$ is the slit width, $D$ the shortest distance between the slit and the screen, $d$ the distance between the $m^{th}$ diffraction maximum and the central maximum, and $λ$ is the wavelength. $D$ and $d$ are measured with scales of least count of $1 cm$ and $1 mm$ , respectively. The values of $λ$ and $m$ are known precisely to be $600 nm$ and $3$ , respectively. The absolute error (in $μ m$ ) in the value of $b$ estimated using the diffraction maximum that occurs for $m = 3$ with $d = 5 mm$ and $D = 1 m$ is ___

JEE Advanced 2022

LEVELJEE Advanced

Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 mm$ . The circular scale has $100$ divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below. \begin{array}{|l|c|c|} \hline \textbf{Measurement condition} & \textbf{Main scale reading} & \textbf{Circular scale reading} \\ \hline \text{Two arms of gauge touching} & & \\ \text{each other without wire} & 0\text{ division} & 4\text{ division} \\ \hline \text{Attempt-1: With wire} & 4\text{ divisions} & 20\text{ divisions} \\ \hline \text{Attempt-2: With wire} & 4\text{ divisions} & 16\text{ divisions} \\ \hline \end{array} What are the diameter and cross-sectional area of the wire measured using the screw gauge?

(A)

2.22 \pm 0.02 mm, π (1.23 \pm 0.02) mm^{2}

(B)

2.22 \pm 0.01 mm, π (1.23 \pm 0.01) mm^{2}

(C)

2.14 \pm 0.02 mm, π (1.14 \pm 0.02) mm^{2}

(D)

2.14 \pm 0.01 mm, π (1.14 \pm 0.01) mm^{2}

JEE Main 2021

LEVELJEE Advanced

The entropy of any system is given by $S = α^{2} β ln [\frac{μ k R}{J β ^{2}} + 3]$ where, $α$ and $β$ are the constants; $μ$ , $J$ , $k$ and $R$ are number of moles, mechanical equivalent of heat, Boltzmann constant and gas constant, respectively. $[Take, S = \frac{d Q}{T}]$ Choose the incorrect option.

(A)

α

and

J

have the same dimensions.

(B)

S, β, k

and

μ R

have the same dimensions.

(C)

S

and

α

have different dimensions.

(D)

α

and

k

have the same dimensions.

JEE Main 2021

LEVELJEE Advanced

Student A and student B used two screw gauges of equal pitch and $100$ equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is $0.322 cm$ . The absolute value of the difference between the final circular scale readings observed by the students A and B is ......... . [Figure shows position of reference O when jaws of screw gauge are closed] Given, pitch $= 0.1 cm$ .

JEE Advanced 2016

LEVELJEE Advanced

In an experiment to determine the acceleration due to gravity $g$ , the formula used for the time period of a periodic motion is $T = 2 π \frac{7 ( R - r )}{5 g}$ . The values of $R$ and $r$ are measured to be $(60 \pm 1) mm$ and $(10 \pm 1) mm$ , respectively. In five successive measurements, the time period is found to be $0.52 s$ , $0.56 s$ , $0.57 s$ , $0.54 s$ and $0.59 s$ . The least count of the watch used for the measurement of time period is $0.01 s$ . Which of the following statement(s) is (are) true?

* Multiple Correct Options

(A)

The error in the measurement of

r

10%

(B)

The error in the measurement of

T

3.57%

(C)

The error in the measurement of

T

2%

(D)

The error in the measurement of

g

11%

JEE Advanced 2015

LEVELJEE Advanced

Planck's 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 options is/are

* Multiple Correct Options

(A)

M \propto c

(B)

M \propto G

(C)

L \propto h

(D)

L \propto G

JEE Advanced 2012

LEVELJEE Advanced

In the determination of Young's modulus $(Y = \frac{4 M Lg}{π l d ^{2}})$ by using Searle's method, a wire of length $L = 2 m$ and diameter $d = 0.5 mm$ is used. For a load $M = 2.5 kg$ , an extension $l = 0.25 mm$ in the length of the wire is observed. Quantities $d$ and $l$ are measured using a screw gauge and a micrometer, respectively. They have the same pitch of $0.5 mm$ . The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the $Y$ measurement is

(A)

due to the errors in the measurements of

d

and

l

are the same

(B)

due to the error in the measurement of

d

is twice that due to the error in the measurement of

l

(C)

due to the error in the measurement of

l

is twice that due to the error in the measurement of

d

(D)

due to the error in the measurement of

d

is four times that due to the error in the measurement of

l

JEE Advanced 2015

LEVELJEE Advanced

In terms of potential difference $V$ , electric current $I$ , permittivity $ε_{0}$ , permeability $μ_{0}$ and speed of light $c$ , the dimensionally correct equations is/are

* Multiple Correct Options

(A)

μ_{0} I^{2} = ε_{0} V^{2}

(B)

ε_{0} I = μ_{0} V

(C)

I = ε_{0} c V

(D)

μ_{0} c I = ε_{0} V

JEE Advanced 2007

LEVELJEE Advanced

A student performs an experiment to determine the Young's modulus of a wire, exactly $2 m$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 mm$ with an uncertainty of $\pm 0.05 mm$ at a load of exactly $1.0 kg$ . The student also measures the diameter of the wire to be $0.4 mm$ with an uncertainty of $\pm 0.01 mm$ . Take $g = 9.8 m/s^{2}$ (exact). The Young's modulus obtained from the reading is close to

(A)

(2.0 \pm 0.3) \times 1 0^{11} N/m^{2}

(B)

(2.0 \pm 0.2) \times 1 0^{11} N/m^{2}

(C)

(2.0 \pm 0.1) \times 1 0^{11} N/m^{2}

(D)

(2.0 \pm 0.05) \times 1 0^{11} N/m^{2}

JEE Advanced 2015

LEVELJEE Advanced

The energy of a system as a function of time $t$ is given as $E (t) = A^{2} exp (- α t)$ , where $α = 0.2 s^{- 1}$ . The measurement of $A$ has an error of $1.25%$ . If the error in the measurement of time is $1.50%$ , the percentage error in the value of $E (t)$ at $t = 5 s$ is

JEE Advanced 2007

LEVELJEE Advanced

Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II.

List-I

(P)

G M_{e} M_{s}

G

— universal gravitational constant,

M_{e}

— mass of the earth,

M_{s}

— mass of the sun.

(Q)

\frac{3 R T}{M}

R

— universal gas constant,

T

— absolute temperature,

M

— molar mass.

(R)

\frac{F ^{2}}{q ^{2} B ^{2}}

F

— force,

q

— charge,

B

— magnetic field.

(S)

\frac{G M _{e}}{R _{e}}

G

— universal gravitational constant,

M_{e}

— mass of the earth,

R_{e}

— radius of the earth.

List-II

(1)

(volt) (coulomb) (metre)

(2)

(kilogram) (metre)

^{3}

(second)

^{- 2}

(3)

(metre)

^{2}

(second)

^{- 2}

(4)

(farad) (volt)

^{2}

(kg)

^{- 1}

JEE Advanced 2011

LEVELJEE Advanced

Comprehension Passage

A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let

N

be the number density of free electrons, each of mass

m

. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. If the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency

ω_{p}

, which is called the plasma frequency. To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency

ω

, where a part of the energy is absorbed and a part of it is reflected. As

ω

approaches

ω_{p}

, all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.

Question 1:

Taking the electronic charge as $e$ and the permittivity as $ε_{0}$ , use dimensional analysis to determine the correct expression for $ω_{p}$ .

(A)

\frac{N e}{m ε _{0}}

(B)

\frac{m ε _{0}}{N e}

(C)

\frac{N e ^{2}}{m ε _{0}}

(D)

\frac{m ε _{0}}{N e ^{2}}

Question 2:

Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons $N \approx 4 \times 1 0^{27} m^{- 3}$ . Take $ε_{0} \approx 1 0^{- 11}$ and $m \approx 1 0^{- 30}$ , where these quantities are in proper SI units.

(A)

800 nm

(B)

600 nm

(C)

300 nm

(D)

200 nm

JEE Advanced 2015

LEVELJEE Advanced

Consider a vernier caliper in which each $1 cm$ on the main scale is divided into $8$ equal divisions and a screw gauge with $100$ divisions on its circular scale. In the vernier callipers, $5$ divisions of the vernier scale coincide with $4$ divisions on the main scale and in the screw gauge, one complete rotation of the circular scale moves it by two divisions on the linear scale. Then

* Multiple Correct Options

(A)

if the pitch of the screw gauge is twice the least count of the vernier caliper, the least count of the screw gauge is

0.01 mm

(B)

if the pitch of the screw gauge is twice the least count of the Vernier caliper, the least count of the screw gauge is

0.005 mm

(C)

if the least count of the linear scale of the screw gauge is twice the least count of the Vernier calipers, the least count of the screw gauge is

0.01 mm

(D)

if the least count of the linear scale of the screw gauge is twice the least count of the vernier caliper, the least count of the screw gauge is

0.005 mm

JEE Advanced 2016

LEVELJEE Advanced

There are two vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. The vernier scale of one of the calipers ( $C_{1}$ ) has 10 equal divisions that correspond to 9 main scale divisions. The vernier scale of the other caliper ( $C_{2}$ ) has 10 equal divisions that correspond to 11 main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by calipers $C_{1}$ and $C_{2}$ respectively, are

Comprehension Passage

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation

z = x / y

. If the errors in

x, y

and

z

are

Δ x, Δ y

and

Δ z

respectively, then

z \pm Δ z = \frac{x \pm Δ x}{y \pm Δ y} = \frac{x}{y} (1 \pm \frac{Δ x}{x}) (1 \pm \frac{Δ y}{y})^{- 1}

The series expansion for

(1 \pm \frac{Δ y}{y})^{- 1}

to first power in

Δ y / y

, is

1 \mp (Δ y / y)

. The relative errors in independent variables are always added. So, the error in

z

will be

Δ z = z (\frac{Δ x}{x} + \frac{Δ y}{y})

The above derivation makes the assumption that

Δ x / x ≪ 1

Δ y / y ≪ 1

. Therefore, the higher powers of these quantities are neglected.

Question 1:

Consider the ratio $r = \frac{( 1 - a )}{( 1 + a )}$ to be determined by measuring a dimensionless quantity $a$ . If the error in the measurement of $a$ is $Δ a$ ( $Δ a / a ≪ 1$ ), then what is the error $Δ r$ in determining $r$ ?

(A)

\frac{Δ a}{( 1 + a ) ^{2}}

(B)

\frac{- 2Δ a}{( 1 + a ) ^{2}}

(C)

\frac{2Δ a}{( 1 - a ) ^{2}}

(D)

\frac{2 a Δ a}{( 1 - a ^{2} )}

Question 2:

In an experiment, the initial number of radioactive nuclei is 3000. It is found that $1000 \pm 40$ nuclei decayed in the first 1.0 s. For $∣ x ∣ ≪ 1$ , $ln (1 + x) = x$ up to first power in $x$ . The error $Δ λ$ , in the determination of the decay constant $λ$ in $s^{- 1}$ , is

A length-scale ( $l$ ) depends on the permittivity ( $ε$ ) of a dielectric material, Boltzmann's 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 expression (s) for $l$ is (are) dimensionally correct?

* Multiple Correct Options

(A)

l = \frac{n q ^{2}}{ε k _{B} T}

(B)

l = \frac{ε k _{B} T}{n q ^{2}}

(C)

l = \frac{q ^{2}}{ε n ^{2/3} k _{B} T}

(D)

l = \frac{q ^{2}}{ε n ^{1/3} k _{B} T}

JEE Advanced 2013

LEVELJEE Advanced

Using the expression $2 d sin θ = λ$ , one calculates the values of $d$ by measuring the corresponding angles $θ$ in the range $0^{\circ}$ to $9 0^{\circ}$ . The wavelength $λ$ is exactly known and the error in $θ$ is constant for all values of $θ$ . As $θ$ increases from $0^{\circ}$

(A)

the absolute error in

d

remains constant

(B)

the absolute error in

d

increases

(C)

the fractional error in

d

remains constant

(D)

the fractional error in

d

decreases

JEE Main 2025

LEVELJEE Advanced

Figure 1 shows the configuration of main scale and Vernier scale before measurement. Fig. 2 shows the configuration corresponding to the measurement of diameter $D$ of a tube. The measured value of $D$ is:

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity $X$ as follows: $[position] = [X^{α}]$ ; $[speed] = [X^{β}]$ ; $[acceleration] = [X^{p}]$ ; $[linear momentum] = [X^{q}]$ ; $[force] = [X^{r}]$ . Then -

* Multiple Correct Options

(A)

α + p = 2 β

(B)

p + q - r = β

(C)

p - q + r = α

(D)

p + q + r = β

JEE Advanced 2022

LEVELJEE Advanced

In a particular system of units, a physical quantity can be expressed in terms of the electric charge $e$ , electron mass $m_{e}$ , Planck's constant $h$ , and Coulomb's constant $k = \frac{1}{4 π ϵ _{0}}$ , where $ϵ_{0}$ is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is $[B] = [e]^{α} [m_{e}]^{β} [h]^{γ} [k]^{δ}$ . The value of $α + β + γ + δ$ is ________.

Micro-Topic Strategy Matrix

Vernier Calipers and Screw Gauge

Errors in Measurement

Significant Figures

Dimensional Analysis

Chapter Elite-20 Challenge Zone

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Planck's 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 options is/are

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In terms of potential difference V, electric current I, permittivity ε0​, permeability μ0​ and speed of light c, the dimensionally correct equations is/are

Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II.

List-I

List-II

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Taking the electronic charge as e and the permittivity as ε0​, use dimensional analysis to determine the correct expression for ωp​.

Comprehension Passage

Planck's 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 options is/are

In terms of potential difference $V$ , electric current $I$ , permittivity $ε_{0}$ , permeability $μ_{0}$ and speed of light $c$ , the dimensionally correct equations is/are

Taking the electronic charge as $e$ and the permittivity as $ε_{0}$ , use dimensional analysis to determine the correct expression for $ω_{p}$ .