JEE Main
Physics
Units & Measurements
Previous Years Questions

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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 dimensional formula of angular impulse is :
The radius $(\mathrm{r})$, length $(l)$ and resistance $(\mathrm{R})$ of a metal wire was measured in the laboratory as \begin{aligned} & \mathrm{r... Consider two physical quantitiesA$$and$$B$$related to each other as$$E=\frac{B-x^2}{A t}$$where$$E, x$$and$$t$$have dimensions of energy, ... The measured value of the length of a simple pendulum is$$20 \mathrm{~cm}$$with$$2 \mathrm{~mm}$$accuracy. The time for 50 oscillations was measur... If the percentage errors in measuring the length and the diameter of a wire are$$0.1 \%$$each. The percentage error in measuring its resistance will... A force is represented by$$F=a x^2+b t^{\frac{1}{2}}$$where$$x=$$distance and$$t=$$time. The dimensions of$$b^2 / a$$are: If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is$$0.5 \mathrm{~mm}$$,... If mass is written as$$m=k \mathrm{c}^{\mathrm{P}} G^{-1 / 2} h^{1 / 2}$$then the value of$$P$$will be : (Constants have their usual meaning with ... Match List I with List II. .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-famil... A physical quantity$$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$$and... The resistance$$R=\frac{V}{I}$$where$$\mathrm{V}=(200 \pm 5) \mathrm{V}$$and$$I=(20 \pm 0.2) \mathrm{A}$$, the percentage error in the measuremen... Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In Vernier calliper if posi... Given below are two statements : Statement (I) : Planck's constant and angular momentum have same dimensions. Statement (II) : Linear momentum and mom... The speed of a wave produced in water is given by v=\lambda^{a} g^{b} \rho^{c}. Where \lambda, g and \rho are wavelength of wave, acceleration d... In the equation$$\left[X+\frac{a}{Y^{2}}\right][Y-b]=\mathrm{R} T, X$$is pressure,$$Y$$is volume,$$\mathrm{R}$$is universal gas constant and$$T...
A body of mass $$(5 \pm 0.5) ~\mathrm{kg}$$ is moving with a velocity of $$(20 \pm 0.4) ~\mathrm{m} / \mathrm{s}$$. Its kinetic energy will be
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If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be :
Given below are two statements : Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances...
In an experiment with vernier callipers of least count $$0.1 \mathrm{~mm}$$, when two jaws are joined together the zero of vernier scale lies right to...
A physical quantity P is given as $$P = {{{a^2}{b^3}} \over {c\sqrt d }}$$ The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and...
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Dimension of $$\frac{1}{\mu_{0} \in_{0}}$$ 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 ...
Two resistances are given as $$\mathrm{R}_{1}=(10 \pm 0.5) \Omega$$ and $$\mathrm{R}_{2}=(15 \pm 0.5) \Omega$$. The percentage error in the measuremen...
If the velocity of light $$\mathrm{c}$$, universal gravitational constant $$\mathrm{G}$$ and Planck's constant $$\mathrm{h}$$ are chosen as fundamenta...
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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 ...
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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...
A travelling microscope has 20 divisions per $$\mathrm{cm}$$ on the main scale while its vernier scale has total 50 divisions and 25 vernier scale div...
In an experiment to find out the diameter of wire using screw gauge, the following observations were noted : (A) Screw moves $$0.5 \mathrm{~mm}$$ on ...
Consider the efficiency of carnot's engine is given by $$\eta=\frac{\alpha \beta}{\sin \theta} \log_e \frac{\beta x}{k T}$$, where $$\alpha$$ and $$\b... The dimensions of$$\left(\frac{\mathrm{B}^{2}}{\mu_{0}}\right)$$will be : (if$$\mu_{0}$$: permeability of free space and$$B$$: magnetic field)... An expression of energy density is given by$$u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$$, where$$\alpha, \beta$$are constants, ... A torque meter is calibrated to reference standards of mass, length and time each with$$5 \%$$accuracy. After calibration, the measured torque with ... In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, t... A screw gauge of pitch$$0.5 \mathrm{~mm}$$is used to measure the diameter of uniform wire of length$$6.8 \mathrm{~cm}$$, the main scale reading is ... The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are$$1 \%, 2 \%$$and$$3 \%$$... If momentum [P], area$$[\mathrm{A}]$$and time$$[\mathrm{T}]$$are taken as fundamental quantities, then the dimensional formula for coefficient of ... If n main scale divisions coincide with (n + 1) vernier scale divisions. The least count of vernier callipers, when each centimetre on the main scale ... The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be : A silver wire has a mass (0.6$$\pm$$0.006) g, radius (0.5$$\pm$$0.005) mm and length (4$$\pm$$0.04) cm. The maximum percentage error in the meas... The dimension of mutual inductance is : An expression for a dimensionless quantity P is given by$$P = {\alpha \over \beta }{\log _e}\left( {{{kt} \over {\beta x}}} \right)$$; where$$\alph...
If $$Z = {{{A^2}{B^3}} \over {{C^4}}}$$, then the relative error in Z will be :
Identify the pair of physical quantities that have same dimensions:
Identify the pair of physical quantities which have different dimensions:
A student determined Young's Modulus of elasticity using the formula $$Y = {{Mg{L^3}} \over {4b{d^3}\delta }}$$. The value of g is taken to be 9.8 m/s...
If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :
Match List - I with List - II. List - I List - II (a) Torque (i) MLT$$^{ - 1}$$ (b) Impuls...
Which of the following equations is dimensionally incorrect?Where t = time, h = height, s = surface tension, $$\theta$$ = angle, $$\rho$$ = density, a...
Match List - I with List - II. List - I List - II (a) $${R_H}$$ (Rydberg constant) (i) $$kg\,{m^{ - 1}}{... If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density : Which of the following is not a dimensionless quantity? If E and H represents the intensity of electric field and magnetising field respectively, then the unit of E/H will be : Match List - I with List - II Choose the most appropriate answer from the options given below :... If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is : In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the cir... If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the for... A physical quantity 'y' is represented by the formula$$y = {m^2}{r^{ - 4}}{g^x}{l^{ - {3 \over 2}}}$$If the percentage errors found in y, m, r, l and... Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 to... The force is given in terms of time t and displacement x by the equation F = A cos Bx + C sin DtThe dimensional formula of$${{AD} \over B}$$is :... If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) in terms of t, v and l is : The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a measurement it was noted that '0' on the vernier scale l... In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1m (measured using ... One main scale division of a vernier callipers is 'a' cm and nth division of the vernier scale coincide with (n$$-$$1)th division of the main scale.... If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of$$\lambda$$where C/V =$$\lambda$$? In a typical combustion engine the workdone by a gas molecule is given by$$W = {\alpha ^2}\beta {e^{{{ - \beta {x^2}} \over {kT}}}}$$, where x is the... If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity$${1 \over {4\pi {\varepsilon _0}}}{{|e{...
Match List - I with List - II : List I List II (a) h (Planck's constant) (i) $$[ML{T^{ - 1}}]$$ ...
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 circu...
The work done by a gas molecule in an isolated system is given by, $$W = \alpha {\beta ^2}{e^{ - {{{x^2}} \over {\alpha kT}}}}$$, where x is the displ...
A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5...
A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete ...
The quantities x = $${1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}$$, y = $${E \over B}$$ and z = $${l \over {CR}}$$ are defined where C-capacitance, ...
A physical quantity z depends on four observables a, b, c and d, as z = $${{{a^2}{b^{{2 \over 3}}}} \over {\sqrt c {d^3}}}$$. The percentages of error...
A quantity x is given by $$\left( {{{IF{v^2}} \over {W{L^4}}}} \right)$$ in terms of moment of inertia I, force F, velocity v, work W and Length L. Th...
Dimensional formula for thermal conductivity is (here K denotes the temperature):
Amount of solar energy received on the earth’s surface per unit area per unit time is defined a solar constant. Dimension of solar constant is :
Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as
If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is
The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the ...
If speed V, area A and force F are chosen as fundamental units, then the dimension of Young’s modulus will be
For the four sets of three measured physical quantities as given below. Which of the following options is correct ? (i) A1 = 24.36, B1 = 0.0724, C1 = ...
A quantity f is given by $$f = \sqrt {{{h{c^5}} \over G}}$$ where c is speed of light, G universal gravitational constant and h is the Planck's const...
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 the circular scale the least co...
The dimension of stopping potential V0 in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' an...
The dimension of $${{{B^2}} \over {2{\mu _0}}}$$, where B is magnetic field and $${{\mu _0}}$$ is the magnetic permeability of vacuum, is :
Which of the following combinations has the dimension of electrical resistance ($$\in$$0 is the permittivity of vacuum and $$\mu$$0 is the permeabi...
In the formula X = 5YZ2 , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?...
The area of a square is 5.29 cm2. The area of 7 such squares taking into account the significant figures is :-
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, respectively. The error in the m...
In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1...
If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear...
In SI units, the dimesions of $$\sqrt {{{{ \in _0}} \over {{\mu _0}}}}$$ is :
Let $$\ell$$, r, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of $${\ell \over {rCV}}$$ in SI unit...
The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 $$\mu$$m diam...
If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young,s modulus will be:
The force of interaction between two atoms is given by F = $$\alpha$$$$\beta$$exp $$\left( { - {{{x^2}} \over {\alpha kt}}} \right)$$; where x is t...
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 cm, respectively. What will be ...
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 of mass is 50 g, the numerica...
Expression for time in terms of G(universal gravitional constant), h (Planck constant) and c (speed of light) is proportional to :
The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully ...
A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is :

## MCQ (More than One Correct Answer)

A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = ...
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