Units & Measurement — JEE Main PYQs

In an experiment to measure focal length (f) of convex lens, the least counts of the measuring scales for the position of object ( u ) and for the position of image ( v ) are $\Delta \mathrm{u}$ and $\Delta \mathrm{v}$, respectively. The error in the measurement of the focal …

What is the dimensional formula of ${\mathrm{ab}}^{-1}$ in the equation $\left(\mathrm{P}+\frac{\mathrm{a}}{{\mathrm{V}}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where letters have their usual meaning.

A vernier callipers has 20 divisions on the vernier scale, which coincides with $19^{\text{th}}$ division on the main scale. The least count of the instrument is 0.1 mm. One main scale division is equal to ______ mm.

If $G$ be the gravitational constant and $u$ be the energy density then which of the following quantity have the dimension as that the $\sqrt{\mathrm{uG}}$ :

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as $4.62\mathrm{s}$, $4.632\mathrm{s}$, $4.6\mathrm{s}$ and $4.64$ s. The arithmetic mean of these reading in correct significant figure is.

To find the spring constant (k) of a spring experimentally, a student commits $2\%$ positive error in the measurement of time and $1\%$ negative error in measurement of mass. The percentage error in determining value of k is :

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1 mm and it has 100 divisions on circular scale. The diameter of the wire is …

In an expression a × $10^{\mathrm{b}}$ :

Young's modulus is determined by the equation given by $Y=49000\frac{\mathrm{m}}{\ell }\frac{\text{ dyne }}{{\mathrm{cm}}^2}$ where $M$ is the mass and $\ell$ is the extension of wire used in the experiment. Now error in Young modules(Y) is estimated by taking data from …

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to 1 mm. The main scale reading is 2 cm and second division of vernier scale coincides with a …

If ${ϵ}_0$ is the permittivity of free space and E is the electric field, then ${\in }_0{E}^2$ has the dimensions :

There are 100 divisions on the circular scale of a screw gauge of pitch 1 mm. With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found the …

Least count of a vernier caliper is $\frac{1}{20\mathrm{N}}$ cm. The value of one division on the main scale is 1 mm. Then the number of divisions of main scale that coincide with N divisions of vernier scale is :

The dimensional formula of latent heat is:

One main scale division of a vernier caliper is equal to $m$ units. If $n^{\text{th }}$ division of main scale coincides with $(\mathrm{n}+1{)}^{\text{th }}$ division of vernier scale, the least count of the vernier caliper is:

The equation of state of a real gas is given by $\left(\mathrm{P}+\frac{\mathrm{a}}{{\mathrm{V}}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where $\mathrm{P},\mathrm{V}$ and T are pressure, volume and temperature respectively and R is the universal gas constant. The dime …

Given below are two statements: one is labelled as Assertion(A) and the other is labelled as Reason (R).
Assertion (A): In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading.
Reason (R): The zero …

A physical quantity Q is found to depend on quantities $a,b,c$ by the relation $Q=\frac{a^4{b}^3}{c^2}$. The percentage error in $a,b$ and c are $3\%$, $4\%$ and $5\%$ respectively. Then, the percentage error in Q is :

Identify the physical quantity that cannot be measured using spherometer :

Given below are two statements :

Statement (I) : Planck's constant and angular momentum have same dimensions.

Statement (II) : Linear momentum and moment of force have same dimensions.
In the light of the above statements, choose the correct answer from the options given below …

The resistance $\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}$ where $\mathrm{V}=(200\pm 5)\mathrm{V}$ and $\mathrm{I}=(20\pm 0.2)\mathrm{A}$, the percentage error in the measurement of R is:

If the percentage errors in measuring the length and the diameter of a wire are $0.1\%$ each. The percentage error in measuring its resistance will be:

A force is represented by $\mathrm{F}={\mathrm{ax}}^2+{\mathrm{bt}}^{1/2}$

Where $\mathrm{x}=$ distance and $\mathrm{t}=$ time. The dimensions of $b^2/a$ are :

Match List - I with List - II.

List - I (Number)
List - II (Significant figure)

Choose the correct answer from the options given below :

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is:

The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as
$\mathrm{r}=(0.35\pm 0.05)\mathrm{cm}$
$\mathrm{R}=(100\pm 10)\mathrm{ohm}$
$l=(15\pm 0.2)\mathrm{cm}$
The percentage error in resistivity of the material of the wire is :

If 50 Vernier divisions are equal to 49 main scale divisions of a travelling microscope and one smallest reading of main scale is 0.5 mm, the Vernier constant of travelling microscope is:

If mass is written as $\mathrm{m}=\mathrm{k}{\mathrm{c}}^{\mathrm{P}}{\mathrm{G}}^{-1/2}{\mathrm{h}}^{1/2}$ then the value of P will be : (Constants have their usual meaning with k a dimensionless constant)

The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is …

Consider two physical quantities A and B related to each other as $E=\frac{B-x^2}{At}$ where $E,x$ and $t$ have dimensions of energy, length and time respectively. The dimension of AB is

Dimension of $\frac{1}{{\mu }_0{ϵ}_0}$ should be equal to

A cylindrical wire of mass $(0.4\pm 0.01)\mathrm{g}$ has length $(8\pm 0.04)\mathrm{cm}$ and radius $(6\pm 0.03)\mathrm{mm}$. The maximum error in its density will be

A 2 meter long scale with least count of 0.2 cm is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at 80 cm mark and lm mark, respectively. The image of the object pin o …

In an experiment with Vernier callipers of least count 0.1 mm , when two jaws are joined together the zero of Vernier scale lies right to the zero of the main scale and $6^{\text{th }}$ division of Vernier scale coincides with the main scale division. While measuring the diame …

A physical quantity $P$ is given as


The percentage error in the measurement of $\mathrm{a},\mathrm{b},\mathrm{c}$ and d are $1\%,2\%,3\%$ and $4\%$ respectively. The percentage error in the measurement of quantity P will be

Given below are two statements :
Statements I : Astronomical unit (Au). Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.
Statements II: Au < Parsec (Pc) < ly
In the light of the above statements. choose the most appropriate answer from the options g …

A body of mass $(5\pm 0.5)$ kg is moving with a velocity of $(20\pm 0.4)$ m/s. Its kinetic energy will be

In the equation $\left[X+\frac{a}{Y^2}\right][Y-b]=\mathrm{R}T,X$ is pressure, $Y$ is volume, R is universal gas constant and $T$ is temperature. The physical quantity equivalent to the ratio $\frac{a}{b}$ is :

The speed of a wave produced in water is given by $v={\lambda }^a{g}^b{\rho }^c$. Where $\lambda ,g$ and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $\mathrm{a},\mathrm{b}$ and c respectively, are :

Two resistances are given as $R_1=(10\pm 0.5)\Omega$ and ${\mathrm{R}}_2=(15\pm 0.5)\Omega$. The percentage error in the measurement of equivalent resistance when they are connected in parallel is

If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be:

$\left(P+\frac{a}{V^2}\right)(V-b)=RT$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a,b,R$ are the constants. The physical quantity, which has dimensional formula as that of …

The frequency ($v$) of an oscillating liquid drop may depend upon radius (r) of the drop, density ($\rho$) of liquid and the surface tension (s) of the liquid as : $v=r^a{\rho }^b{s}^c$. The values of $a,b$ and $c$ respectively are

Match List I with List II

List I:
A. Young's Modulus (Y)
B. Co-efficient of Viscosity ($\eta$)
C. Planck's Constant (h)
D. Work Function $(\varphi )$

List II:
I. $[\mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}]$
II. $[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-1}]$
III. …

The equation of a circle is given by $x^2+y^2=a^2$, where a is the radius. If the equation is modified to change the origin other than $(0,0)$, then find out the correct dimensions of A and B in a new equation: $(x-At{)}^2+(y-\frac{t}{B}{)}^2=a^2$.
The dimensions of $t$ i …

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25 mm and apparent thickness of the glass slab at 5.00 mm. Travelling microscope has 20 divisions in one cm on m …

In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by 0.5 mm on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two studs are brought in contact with each other. When a …

If the velocity of light c, universal gravitational constant G and planck's constant h are chosen as fundamental quantities. The dimensions of mass in the new system is:

The dimensions of $\left(\frac{{\mathrm{B}}^2}{{\mu }_0}\right)$ will be :
(if ${\mu }_0$ : permeability of free space and
B : magnetic field)

Consider the efficiency of Carnot's engine is given by $\eta =\frac{\alpha \beta }{\sin \theta }{\log }_{\mathrm{e}}\frac{\beta \mathrm{x}}{\mathrm{kT}}$, where $\alpha$ and $\beta$ are constants. If T is temperature, k is Boltzman constant, $\theta$ is angular displacement …