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## Units & Measurements

### Physics

#### Previous Years Questions

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Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 \mathrm{~mm}$....
JEE Advanced 2022 Paper 2 Online
The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond t...
JEE Advanced 2021 Paper 1 Offline
In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of e...
JEE Advanced 2018 Paper 1 Offline
If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any...
JEE Advanced 2018 Paper 1 Offline
If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any...
JEE Advanced 2018 Paper 1 Offline
In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of e...
JEE Advanced 2018 Paper 1 Offline
A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of...
JEE Advanced 2017 Paper 2 Offline
There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. The Vernier sc...
JEE Advanced 2016 Paper 2 Offline
Match List I with List II and select the correct answer using the codes given below the lists: List I P. Boltzmann Const...
JEE Advanced 2013 Paper 2 Offline
The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Ve...
JEE Advanced 2013 Paper 1 Offline
In the determination of Young's modulus $$\left( {Y = {{4MLg} \over {\pi l{d^2}}}} \right)$$ by using Searle's method, a...
IIT-JEE 2012 Paper 1 Offline
A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fi...
IIT-JEE 2011 Paper 1 Offline
A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fi...
IIT-JEE 2011 Paper 1 Offline
The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gaug...
IIT-JEE 2011 Paper 2 Offline
A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 ...
IIT-JEE 2010 Paper 2 Offline
Student I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. T...
IIT-JEE 2008
Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are...
IIT-JEE 2007
A student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long, by Searle's method. In a ...
IIT-JEE 2007
In a screw gauge, the zero of main scale coincides with the fifth division of circular scale in figure (i).The circular ...
IIT-JEE 2006
A student performs an experiment for determination of $$\mathrm g\left(=\frac{4\mathrm\pi^2\mathcal l}{\mathrm T^2}\righ... IIT-JEE 2006 Which of the following set have different dimensions? IIT-JEE 2005 Screening A wire of length$$l = 6 \pm 0.06$$cm and$$r = 0.5 \pm 0.005$$cm and mass$$m = 0.3 \pm 0.003$$gm. Maximum percentag... IIT-JEE 2004 Screening Pressure depends on distance as,$$P = {\alpha \over \beta }\exp \left( { - {{\alpha z} \over {k\theta }}} \right)$$, w... IIT-JEE 2004 Screening A cube has a side of length 1.2 ✕ 10-2 m. Calculate its volume. IIT-JEE 2003 Screening A quantity X is given by$${\varepsilon _0}L{{\Delta V} \over {\Delta t}}$$where$${\varepsilon _0}$$is the permittivi... IIT-JEE 2001 Screening The dimension of$$\left( {{1 \over 2}} \right){\varepsilon _0}{E^2}$$($${\varepsilon _0}$$: permittivity of free spa... IIT-JEE 2000 Screening ## Numerical More In a particular system of units, a physical quantity can be expressed in terms of the electric charge e, electron mass... JEE Advanced 2022 Paper 2 Online An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal length of a conv... JEE Advanced 2019 Paper 2 Offline A steel wire of diameter$$0.5mm$$and Young's modulus$$2 \times {10^{11}}\,\,N{m^{ - 2}}$$carries a load of mass... JEE Advanced 2018 Paper 2 Offline The energy of a system as a function of time t is given as E(t) =$${A^2}\exp \left( { - \alpha t} \right)$$, where$$\a...
JEE Advanced 2015 Paper 2 Offline
During Searle's experiment, zero of the Vernier scale lies between 3.20 $$\times$$ 10-2 m and 3.25 $$\times$$ 10-2 m...
JEE Advanced 2014 Paper 1 Offline
To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional...
JEE Advanced 2014 Paper 1 Offline

## MCQ (More than One Correct Answer)

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A physical quantity $$\overrightarrow S$$ is defined as $$\overrightarrow S = (\overrightarrow E \times \overrightarr... JEE Advanced 2021 Paper 2 Online Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one p... JEE Advanced 2020 Paper 1 (Offline) Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, wh... JEE Advanced 2019 Paper 1 Offline In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic moti... JEE Advanced 2016 Paper 2 Offline A length-scale (l) depends on the permittivity ($$\varepsilon $$) of a dielectric material, Boltzmann constant (kB), the... JEE Advanced 2016 Paper 1 Offline In terms of potential difference V, electric current I, permittivity$${\varepsilon _0}$$, permeability$${\mu _0}$$and... JEE Advanced 2015 Paper 2 Offline Consider a Vernier callipers in which each 1 cm on the main scale is divided into 8 equal divisions and a screw gauge wi... JEE Advanced 2015 Paper 1 Offline Planck's constant h, speed of light c and gravitational constant G are used to form a unit of length L and a unit of mas... JEE Advanced 2015 Paper 1 Offline A student is performing an experiment using a resonance column and a tuning fork of frequency 244 s$$-$$1. He is told th... JEE Advanced 2014 Paper 1 Offline A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop wa... IIT-JEE 2010 Paper 1 Offline Let [$${\mathrm\varepsilon}_\mathrm o$$] denote the dimentional formula of the permittivity of the vacuum, and [$$\mu_o\$...
IIT-JEE 1998
The SI unit of inductance, the henry can be written as
IIT-JEE 1998
The pairs of physical quantities that have the same dimensions is (are):
IIT-JEE 1995 Screening
The dimensions of the quantities in one ( or more ) of the following pairs are the same. Identify the pair(s)
IIT-JEE 1986

## Subjective

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The side of a cube is measured by vernier callipers (10 divisions of a vernier scale coincide with 9 divisions of main s...
IIT-JEE 2005
A screw gauge having 100 equal divisions and a pitch of length 1 mm is used to measure the diameter of a wire of length ...
IIT-JEE 2004
In Searle's experiment, which is used to find Young's Modulus of elasticity, the diameter of experimental wire is D = 0....
IIT-JEE 2004
If nth divisions of the main scale coincide with (n+1)th divisions of vernier scale. Given one main scale division is eq...
IIT-JEE 2003
Column - I gives the three physical quantities. Select the appropriate units for the choices given in Column - II. Some ...
IIT-JEE 1990
Match the physical quantities given in column I with dimension expressed in terms of mass (M), length (L), time (T), and...
IIT-JEE 1983
Write the dimensions of the followings in terms of mass, time, length and charge (i) magnetic flux (ii) rigidity modulus...
IIT-JEE 1982
A gas bubble, from an explosion under water, oscillates with a period T proportional to padbEc. Where 'P' is the static ...
IIT-JEE 1981
Give the MKS units for each of the following quantities. (i) Young's modulus (ii) Magnetic Induction (iii) Power of a le...
IIT-JEE 1980

## Fill in the Blanks

More
The equation of state for real gas is given by $$\left( {P + {a \over {{V^2}}}} \right)\left( {V - b} \right) = RT$$. Th...
IIT-JEE 1997
In the formula X = 3YZ2, X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y...
IIT-JEE 1988
Plank' constant has dimension __________.
IIT-JEE 1985

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