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## Units & Measurements

### Physics

#### Previous Years Questions

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The dimensions of $$\left(\frac{\mathrm{B}^{2}}{\mu_{0}}\right)$$ will be : (if $$\mu_{0}$$ : permeability of free space...
JEE Main 2022 (Online) 28th July Morning Shift
An expression of energy density is given by $$u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$$, where $$\... JEE Main 2022 (Online) 27th July Evening Shift A torque meter is calibrated to reference standards of mass, length and time each with$$5 \%$$accuracy. After calibrat... JEE Main 2022 (Online) 27th July Morning Shift In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernie... JEE Main 2022 (Online) 26th July Evening Shift A screw gauge of pitch$$0.5 \mathrm{~mm}$$is used to measure the diameter of uniform wire of length$$6.8 \mathrm{~cm}...
JEE Main 2022 (Online) 26th July Morning Shift
The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit ar...
JEE Main 2022 (Online) 25th July Evening Shift
If momentum [P], area $$[\mathrm{A}]$$ and time $$[\mathrm{T}]$$ are taken as fundamental quantities, then the dimension...
JEE Main 2022 (Online) 25th July Morning Shift
If n main scale divisions coincide with (n + 1) vernier scale divisions. The least count of vernier callipers, when each...
JEE Main 2022 (Online) 30th June Morning Shift
Identify the pair of physical quantities which have different dimensions:
JEE Main 2022 (Online) 24th June Morning Shift
Identify the pair of physical quantities that have same dimensions:
JEE Main 2022 (Online) 24th June Evening Shift
If $$Z = {{{A^2}{B^3}} \over {{C^4}}}$$, then the relative error in Z will be :
JEE Main 2022 (Online) 25th June Morning Shift
The dimension of mutual inductance is :
JEE Main 2022 (Online) 26th June Evening Shift
An expression for a dimensionless quantity P is given by $$P = {\alpha \over \beta }{\log _e}\left( {{{kt} \over {\beta... JEE Main 2022 (Online) 26th June Morning Shift A silver wire has a mass (0.6$$\pm$$0.006) g, radius (0.5$$\pm$$0.005) mm and length (4$$\pm$$0.04) cm. The maximu... JEE Main 2022 (Online) 27th June Morning Shift The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be : JEE Main 2022 (Online) 27th June Evening Shift A student determined Young's Modulus of elasticity using the formula$$Y = {{Mg{L^3}} \over {4b{d^3}\delta }}$$. The val... JEE Main 2021 (Online) 1st September Evening Shift If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be : JEE Main 2021 (Online) 31st August Evening Shift Which of the following equations is dimensionally incorrect?Where t = time, h = height, s = surface tension,$$\theta$$... JEE Main 2021 (Online) 31st August Morning Shift Match List - I with List - II. List - I List - II (a) Torque (i) MLT$$^{ -...
JEE Main 2021 (Online) 31st August Morning Shift
An object is placed at the focus of concave lens having focal length f. What is the magnification and distance of the im...
JEE Main 2021 (Online) 31st August Morning Shift
If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of densit...
JEE Main 2021 (Online) 27th August Evening Shift
Match List - I with List - II. List - I List - II (a) $${R_H}$$ (Rydberg constant)...
JEE Main 2021 (Online) 27th August Evening Shift
If E and H represents the intensity of electric field and magnetising field respectively, then the unit of E/H will be :
JEE Main 2021 (Online) 27th August Morning Shift
Which of the following is not a dimensionless quantity?
JEE Main 2021 (Online) 27th August Morning Shift
If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is :
JEE Main 2021 (Online) 26th August Evening Shift
Match List - I with List - II Choose the most appropriate answer from the options given below :...
JEE Main 2021 (Online) 26th August Evening Shift
If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then ...
JEE Main 2021 (Online) 26th August Morning Shift
In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. The...
JEE Main 2021 (Online) 26th August Morning Shift
A physical quantity 'y' is represented by the formula $$y = {m^2}{r^{ - 4}}{g^x}{l^{ - {3 \over 2}}}$$If the percentage ...
JEE Main 2021 (Online) 27th July Evening Shift
Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gau...
JEE Main 2021 (Online) 27th July Morning Shift
The force is given in terms of time t and displacement x by the equation F = A cos Bx + C sin DtThe dimensional formula ...
JEE Main 2021 (Online) 25th July Evening Shift
If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) i...
JEE Main 2021 (Online) 20th July Evening Shift
The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a measurement it was noted t...
JEE Main 2021 (Online) 17th March Morning Shift
In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) ...
JEE Main 2021 (Online) 16th March Evening Shift
One main scale division of a vernier callipers is 'a' cm and nth division of the vernier scale coincide with (n $$-$$ 1)...
JEE Main 2021 (Online) 16th March Morning Shift
If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of $$\lambda$$ where C/V = $$\la... JEE Main 2021 (Online) 26th February Evening Shift In a typical combustion engine the workdone by a gas molecule is given by$$W = {\alpha ^2}\beta {e^{{{ - \beta {x^2}} \...
JEE Main 2021 (Online) 26th February Morning Shift
If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity $${1 \over... JEE Main 2021 (Online) 25th February Evening Shift The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between t... JEE Main 2021 (Online) 25th February Morning Slot Match List - I with List - II : List I List II (a) h (Planck's constant) (i) ... JEE Main 2021 (Online) 25th February Morning Slot The period of oscillation of a simple pendulum is$$T = 2\pi \sqrt {{L \over g}} $$. Measured value of 'L' is 1.0 m from... JEE Main 2021 (Online) 24th February Evening Slot The work done by a gas molecule in an isolated system is given by,$$W = \alpha {\beta ^2}{e^{ - {{{x^2}} \over {\alpha ...
JEE Main 2021 (Online) 24th February Morning Slot
A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the foll...
JEE Main 2020 (Online) 6th September Evening Slot
A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, pr...
JEE Main 2020 (Online) 6th September Morning Slot
A physical quantity z depends on four observables a, b, c and d, as z = $${{{a^2}{b^{{2 \over 3}}}} \over {\sqrt c {d^3}... JEE Main 2020 (Online) 5th September Morning Slot A quantity x is given by$$\left( {{{IF{v^2}} \over {W{L^4}}}} \right)$$in terms of moment of inertia I, force F, veloc... JEE Main 2020 (Online) 4th September Evening Slot Dimensional formula for thermal conductivity is (here K denotes the temperature): JEE Main 2020 (Online) 4th September Morning Slot Amount of solar energy received on the earth’s surface per unit area per unit time is defined a solar constant. Dimensio... JEE Main 2020 (Online) 3rd September Evening Slot Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It sho... JEE Main 2020 (Online) 3rd September Morning Slot If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energ... JEE Main 2020 (Online) 2nd September Evening Slot The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10 divisions and coi... JEE Main 2020 (Online) 2nd September Morning Slot If speed V, area A and force F are chosen as fundamental units, then the dimension of Young’s modulus will be JEE Main 2020 (Online) 2nd September Morning Slot For the four sets of three measured physical quantities as given below. Which of the following options is correct ? (i) ... JEE Main 2020 (Online) 9th January Evening Slot If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on t... JEE Main 2020 (Online) 9th January Morning Slot A quantity f is given by$$f = \sqrt {{{h{c^5}} \over G}} $$where c is speed of light, G universal gravitational consta... JEE Main 2020 (Online) 9th January Morning Slot The dimension of stopping potential V0 in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and... JEE Main 2020 (Online) 8th January Morning Slot The dimension of$${{{B^2}} \over {2{\mu _0}}}$$, where B is magnetic field and$${{\mu _0}}$$is the magnetic permeabi... JEE Main 2020 (Online) 7th January Evening Slot Which of the following combinations has the dimension of electrical resistance ($$ \in $$0 is the permittivity of vacuum... JEE Main 2019 (Online) 12th April Morning Slot In the formula X = 5YZ2 , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensio... JEE Main 2019 (Online) 10th April Evening Slot The area of a square is 5.29 cm2. The area of 7 such squares taking into account the significant figures is :-... JEE Main 2019 (Online) 9th April Evening Slot In the density measurement of a cube, the mass and edge length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01) m, re... JEE Main 2019 (Online) 9th April Morning Slot If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the ... JEE Main 2019 (Online) 8th April Evening Slot In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is ... JEE Main 2019 (Online) 8th April Evening Slot In SI units, the dimesions of$$\sqrt {{{{ \in _0}} \over {{\mu _0}}}} $$is : JEE Main 2019 (Online) 8th April Morning Slot Let$$\ell $$, r, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of$${\...
JEE Main 2019 (Online) 12th January Evening Slot
The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale requir...
JEE Main 2019 (Online) 12th January Morning Slot
If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young,s modulus will ...
JEE Main 2019 (Online) 11th January Evening Slot
The force of interaction between two atoms is given by F = $$\alpha$$$$\beta$$exp $$\left( { - {{{x^2}} \over {\alpha ... JEE Main 2019 (Online) 11th January Morning Slot The diameter and height of a cylinder are measured by a meter scale to be 12.6$$ \pm $$0.1 cm and 34.2$$ \pm $$0.1 c... JEE Main 2019 (Online) 10th January Evening Slot The density of a material in SI units is 128 kg m–3 . In certain units in which the unit of length is 25 cm and the unit... JEE Main 2019 (Online) 10th January Morning Slot The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. ... JEE Main 2019 (Online) 9th January Evening Slot Expression for time in terms of G(universal gravitional constant), h (Planck constant) and c (speed of light) is proport... JEE Main 2019 (Online) 9th January Evening Slot A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume rema... JEE Main 2019 (Online) 9th January Morning Slot The relative uncertainly in the period of a satellite orbiting around the earth is 10-2. If the relative uncertainty in ... JEE Main 2018 (Online) 16th April Morning Slot The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physica... JEE Main 2018 (Online) 16th April Morning Slot The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined... JEE Main 2018 (Online) 15th April Evening Slot In a screw gauge,$$5$$complete rotations of the screw cause it to move a linear distance of$$0.25cm.$$There are... JEE Main 2018 (Online) 15th April Morning Slot The relative error in the determination of the surface area of sphere is$$\alpha $$. Then the relative error in the de... JEE Main 2018 (Online) 15th April Morning Slot In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cel... JEE Main 2018 (Offline) The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the... JEE Main 2018 (Offline) A physical quantity P is described by the relation P = a$$^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em...
JEE Main 2017 (Online) 9th April Morning Slot
Time (T), velocity (C) and angular momentum (h) are chosen as fundamentalquantities instead of mass, length and time. In...
JEE Main 2017 (Online) 8th April Morning Slot
The following observations were taken for determining surface tension T of water by capillary method: diameter of capill...
JEE Main 2017 (Offline)
In the following ‘I’ refers to current and other symbols have their usual meaning. Choose the option that corresponds to...
JEE Main 2016 (Online) 9th April Morning Slot
A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin s...
JEE Main 2016 (Offline)
A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s...
JEE Main 2016 (Offline)
The period of oscillation of a simple pendulum is $$T = 2\pi \sqrt {{L \over g}}$$. Measured value of L is 20.0 cm kno...
JEE Main 2015 (Offline)
A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?
JEE Main 2014 (Offline)
Let [$${\varepsilon _0}$$] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = ti...
JEE Main 2013 (Offline)
A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading: 58.5 degree Ve...
AIEEE 2012
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across ...
AIEEE 2012
A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm Circula...
AIEEE 2011
The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 $$\times$$ 10–3 are
AIEEE 2010
In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coin...
AIEEE 2009
An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment dista...
AIEEE 2008
Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of di...
AIEEE 2008
A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms−1. The magnitude of its momentum is recor...
AIEEE 2008
The dimension of magnetic field in M, L, T and C (coulomb) is given as
AIEEE 2008
Out of the following pair, which one does NOT have identical dimensions is
AIEEE 2005
Which one of the following represents the correct dimensions of the coefficient of viscosity?
AIEEE 2004
The physical quantities not having same dimensions are
AIEEE 2003
Dimensions of $${1 \over {{\mu _0}{\varepsilon _0}}}$$, where symbols have their usual meaning, are
AIEEE 2003
Identify the pair whose dimensions are equal
AIEEE 2002

## Numerical

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The one division of main scale of Vernier callipers reads $$1 \mathrm{~mm}$$ and 10 divisions of Vernier scale is equal ...
JEE Main 2022 (Online) 27th July Morning Shift
A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the...
JEE Main 2022 (Online) 24th June Morning Shift
For $$z = {a^2}{x^3}{y^{{1 \over 2}}}$$, where 'a' is a constant. If percentage error in measurement of 'x' and 'y' are ...
JEE Main 2022 (Online) 25th June Evening Shift
A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on ...
JEE Main 2022 (Online) 26th June Evening Shift
In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coinci...
JEE Main 2022 (Online) 26th June Morning Shift
A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm a...
JEE Main 2022 (Online) 28th June Evening Shift
The Vernier constant of Vernier callipers is 0.1 mm and it has zero error of ($$-$$0.05) cm. While measuring diameter of...
JEE Main 2022 (Online) 29th June Evening Shift
The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the vernier cal...
JEE Main 2021 (Online) 31st August Evening Shift
The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy supplied to a simple pendulum to...
JEE Main 2021 (Online) 26th August Evening Shift
A 16 $$\Omega$$ wire is bend to form a square loop. A 9V supply having internal resistance of 1$$\Omega$$ is connected a...
JEE Main 2021 (Online) 25th July Evening Shift
Student A and student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a...
JEE Main 2021 (Online) 25th July Morning Shift
Three students S1, S2 and S3 perform an experiment for determining the acceleration due to gravity (g) using a simple pe...
JEE Main 2021 (Online) 22th July Evening Shift
The radius of a sphere is measured to be (7.50 $$\pm$$ 0.85) cm. Suppose the percentage error in its volume is x. The va...
JEE Main 2021 (Online) 18th March Evening Shift
The resistance R = $${V \over I}$$, where V = (50 $$\pm$$ 2)V and I = (20 $$\pm$$ 0.2)A. The percentage error in R is 'x...
JEE Main 2021 (Online) 16th March Morning Shift
The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the densi...
JEE Main 2020 (Online) 6th September Morning Slot

## MCQ (More than One Correct Answer)

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A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But w...
JEE Main 2016 (Online) 10th April Morning Slot

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