Units & Measurements · Physics · JEE Main

The de-Broglie wavelength associated with a particle of mass $$m$$ and energy $$E$$ is $$h / \sqrt{2 m E}$$. The dimensional formula for Planck's cons...

The dimensional formula of latent heat is :

One main scale division of a vernier caliper is equal to $$\mathrm{m}$$ units. If $$\mathrm{n}^{\text {th }}$$ division of main scale coincides with $...

If $$\epsilon_{\mathrm{o}}$$ is the permittivity of free space and $$\mathrm{E}$$ is the electric field, then $$\epsilon_{\mathrm{o}} \mathrm{E}^2$$ h...

There are 100 divisions on the circular scale of a screw gauge of pitch $$1 \mathrm{~mm}$$. With no measuring quantity in between the jaws, the zero o...

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

In an expression $$a \times 10^b$$ :

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 ...

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $$4^{\text {th }}$$ division coincides e...

In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division $$=49 \math...

To find the spring constant $$(k)$$ of a spring experimentally, a student commits $$2 \%$$ positive error in the measurement of time and $$1 \%$$ nega...

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While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is $$1 \mathrm{~mm}$$ and circular scale read...

What is the dimensional formula of $$a b^{-1}$$ in the equation $$\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\math...

A vernier callipers has 20 divisions on the vernier scale, which coincides with $$1^{\text {th }}$$ division on the main scale. The least count of the...

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as $$4.62 \mathrm{~s}, 4.632 \mat...

Applying the principle of homogeneity of dimensions, determine which one is correct, where $$T$$ is time period, $$G$$ is gravitational constant, $$M$...

The equation of stationary wave is : $$y=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right) \t...

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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 quantities $$A$$ 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 ...

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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 ...

Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as $${v_2} = {n \over {{m^2}}}{v_1}$$ and $${a_2} = {{{a_1}} \over {mn}}...

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

If speed V, area A and force F are chosen as fundamental units, then the dimension of Young’s modulus will be

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 ...

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 = ...

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...

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...

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...

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 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...

In SI units, the dimensions 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 :

The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A = $${{{P^3}{Q^2}}...

The relative uncertainly in the period of a satellite orbiting around the earth is 10-2. If the relative uncertainty in the radius of the orbit is neg...

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 relative errors in measuring ...

The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination o...

In a screw gauge, $$5$$ complete rotations of the screw cause it to move a linear distance of $$0.25$$ $$cm.$$ There are $$100$$ circular scale divisi...

The relative error in the determination of the surface area of sphere is $$\alpha $$. Then the relative error in the determination of its volume is :

A physical quantity P is described by the relation P = a$$^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptsty...

Time (T), velocity (C) and angular momentum (h) are chosen as fundamentalquantities instead of mass, length and time. In terms of these, the dimension...

The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D = 1.25 $$\times$$ 10-2 ...

In the following ‘I’ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical ...

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 and 92 s. If the minimum divi...

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 sheet of Aluminium. Before star...

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

Let [$${\varepsilon _0}$$] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, t...

A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading: 58.5 degree Vernier scale reading : 09 divis...

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors i...

A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm Circular scale reading : 52 divisions...

The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 $$ \times $$ 10–3 are

In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of ...

The dimension of magnetic field in M, L, T and C (coulomb) is given as

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 recorded as

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 divisions on the circular scale ...

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by

Out of the following pair, which one does NOT have identical dimensions is

Which one of the following represents the correct dimensions of the coefficient of viscosity?

Dimensions of $${1 \over {{\mu _0}{\varepsilon _0}}}$$, where symbols have their usual meaning, are

The physical quantities not having same dimensions are

Identify the pair whose dimensions are equal

In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by $$0.5 \mathrm{~mm}$$ on a complete rotation of the circula...

In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of $$0.5 \mathrm{~s}$$ is measured from time of 100 oscill...

The one division of main scale of Vernier callipers reads $$1 \mathrm{~mm}$$ and 10 divisions of Vernier scale is equal to the 9 divisions on main sca...

The Vernier constant of Vernier callipers is 0.1 mm and it has zero error of ($$-$$0.05) cm. While measuring diameter of a sphere, the main scale read...

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 and 1.20 mm. The percentage err...

A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scal...

In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coincides with nineth main scale div...

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 4% and 12% respectively, then ...

The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the vernier callipers, are equal to 10 divisi...

The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy supplied to a simple pendulum to known mass 'm' to undertake o...

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 ...

Three students S1, S2 and S3 perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different len...

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 value of x, to the nearest x, is...

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'%. The value of 'x' to the ne...

The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is $$\left( {...

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 = ...