Units & Measurement · Physics · NEET

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MCQ (Single Correct Answer)

1

A balloon is made of a material of surface tension $S$ and its inflation outlet (from where gas is filled in it) has small area $A$. It is filled with a gas of density $\rho$ and takes a spherical shape of radius $R$. When the gas is allowed to flow freely out of it, its radius $r$ changes from $R$ to 0 (zero) in time $T$. If the speed $v(r)$ of gas coming out of the balloon depends on $r$ as $r^\alpha$ and $T \propto S^\alpha A^\beta \rho^\gamma R^\delta$ then

NEET 2025
2

A physical quantity $P$ is related to four observations $a, b, c$ and $d$ as follows:

$$P=a^3 b^2 / c \sqrt{d}$$

The percentage errors of measurement in $a, b, c$ and $d$ are $1 \%, 3 \%, 2 \%$, and $4 \%$ respectively. The percentage error in the quantity $P$ is

NEET 2025
3

Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its 10 Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least division in the M.S. is 0.1 cm and the zero of V.S. is at $x=0.1 \mathrm{~cm}$ when the jaws of Vernier callipers are closed. If the main scale reading for the diameter is $M=5 \mathrm{~cm}$ and the number of coinciding vernier division is 8 , the measured diameter after zero error correction, is

NEET 2025
4

In an electrical circuit, the voltage is measured as $$V=(200 \pm 4)$$ volt and the current is measured as $$I=(20 \pm 0.2)$$ A. The value of the resistance is:

NEET 2024 (Re-Examination)
5

The pitch of an error free screw gauge is $$1 \mathrm{~mm}$$ and there are 100 divisions on the circular scale. While measuring the diameter of a thick wire, the pitch scale reads $$1 \mathrm{~mm}$$ and $$63^{\text {rd }}$$ division on the circular scale coincides with the reference line. The diameter of the wire is:

NEET 2024 (Re-Examination)
6

The potential energy of a particle moving along $$x$$-direction varies as $$V=\frac{A x^2}{\sqrt{x}+B}$$. The dimensions of $$\frac{A^2}{B}$$ are:

NEET 2024 (Re-Examination)
7

In a vernier callipers, $$(N+1)$$ divisions of vernier scale coincide with $$N$$ divisions of main scale. If $$1 \mathrm{~MSD}$$ represents $$0.1 \mathrm{~mm}$$, the vernier constant (in $$\mathrm{cm}$$) is:

NEET 2024
8

The quantities which have the same dimensions as those of solid angle are:

NEET 2024
9

A force defined by $$F=\alpha t^2+\beta t$$ acts on a particle at a given time $$t$$. The factor which is dimensionless, if $$\alpha$$ and $$\beta$$ are constants, is:

NEET 2024
10

The diameter of a spherical bob, when measured with vernier callipers yielded the following values : $$3.33 \mathrm{~cm}, 3.32 \mathrm{~cm}, 3.34 \mathrm{~cm}, 3.33 \mathrm{~cm}$$ and $$3.32 \mathrm{~cm}$$. The mean diameter to appropriate significant figures is :

NEET 2023 Manipur
11

The mechanical quantity, which has dimensions of reciprocal of mass $$(\mathrm{M}^{-1})$$ is :

NEET 2023 Manipur
12

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are :

NEET 2023
13

A metal wire has mass $$(0.4 \pm 0.002) ~\mathrm{g}$$, radius $$(0.3 \pm 0.001) ~\mathrm{mm}$$ and length $$(5 \pm 0.02) ~\mathrm{cm}$$. The maximum possible percentage error in the measurement of density will nearly be :

NEET 2023
14

The physical quantity that has the same dimensional formula as pressure is

NEET 2022 Phase 2
15

The percentage error in the measurement of g is : (Given that $$g = {{4{\pi ^2}L} \over {{T^2}}}$$, $$L = (10\, \pm \,0.1)$$ cm, $$T = (100\, \pm \,1)$$ s)

NEET 2022 Phase 2
16

The dimensions [MLT$$-$$2A$$-$$2] belong to the

NEET 2022 Phase 1
17

Plane angle and solid angle have

NEET 2022 Phase 1
18

The area of a rectangular field (in m2) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is

NEET 2022 Phase 1
19
The E and G respectively denote energy and gravitational constant, then $${E \over G}$$ has the dimensions of :
NEET 2021
20
A screw gauge gives the following readings when used to measure the diameter of a wire

Main scale reading : 0 mm

Circular scale reading : 52 divisions

Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is :
NEET 2021
21
If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.
NEET 2021
22
A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale.
The pitch of the screw gauge is :
NEET 2020 Phase 1
23
Taking into account of the significant figures, what is the value of $$9.99 m - 0.0099m$$?
NEET 2020 Phase 1
24
Dimensions of stress are :
NEET 2020 Phase 1
25
The energy required to break one bond in DNA is 10-20 J. This value in eV is nearly :
NEET 2020 Phase 1
26
In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2 %, 3 %and 4 % respectively. Then the maximum percentage of error in the measurement X, where
X = $${{{A^2}{B^{1/2}}} \over {{C^{1/3}}{D^3}}}$$, will be :
NEET 2019
27
A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of –0.004 cm, the correct diameter of the ball is
NEET 2018
28
A physical quantity of the dimensions of length that can be formed out of c, G and $${{{e^2}} \over {4\pi {\varepsilon _0}}}$$ is [c is velocity of light, G is the universal constant of gravitation and e is charge]
NEET 2017
29
Planck's constant (h), speed of light in vacuum (c) and Newton's gravitional constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length ?
NEET 2016 Phase 2
30
If dimensions of critical velocity $$\upsilon $$c of a liquid flowing through a tube are expressed as $$\left[ {{\eta ^x}{\rho ^y}{r^z}} \right]$$ where $$\eta ,\rho $$ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by
AIPMT 2015
31
If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be
AIPMT 2015 Cancelled Paper
32
If force (F), velocity (V) and time (T) are taken as fundamental units, then dimensions of mass are
AIPMT 2014
33
The pair of quantities having same dimensions is
NEET 2013 (Karnataka)
34
If an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively.

Quantity P is calculated as follows P $$ = {{{a^3}{b^2}} \over {cd}}$$ % error in P is
NEET 2013
35
The dimensions of $${\left( {{\mu _0}{\varepsilon _0}} \right)^{ - 1/2}}$$ are
AIPMT 2012 Mains
36
The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are
AIPMT 2012 Prelims
37
The density of a material in CGS system of units is 4 g cm$$-$$3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be
AIPMT 2011 Mains
38
The dimensions of $${\left( {{\mu _0}{\varepsilon _0}} \right)^{ - 1/2}}$$ are
AIPMT 2011 Prelims
39
A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is
AIPMT 2010 Mains
40
The dimension of $${1 \over 2}{\varepsilon _0}{E^2}$$, where $${\varepsilon _0}$$ is permittivity of free space and E is electric field, is
AIPMT 2010 Prelims
41
If the dimensions of a physical quantity are given by MaLbTc, then the physical quantity will be
AIPMT 2009
42
If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be
AIPMT 2008
43
Which two of the following five physical parameters have the same dimensions ?
1.  Energy density
2.  Refractive index
3.  Dielectric constant
4.  Young's modulus
5.  Magnetic field
AIPMT 2008
44
Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be
AIPMT 2007
45
The velocity v of a particle at time t is given by v = at + $${b \over {t + c}}$$, where a, b and c are constants. The dimensions of a, b and c are
AIPMT 2006
46
The ratio of the dimensions of Planck's constant and that of moment of inertia is the dimensions of
AIPMT 2005
47
The unit of permittyvity of free space, $${\varepsilon _0}$$, is
AIPMT 2004
48
The dimensions of universal gravitational constant are
AIPMT 2004
49
The dimensions of Planck's constant equals to that of
AIPMT 2001
50
Which pair do not have equal dimensions ?
AIPMT 2000
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