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Units & Measurements

230 Questions
All Exams JEE Mains JEE Advanced TS-EAMCET AP-EAPCET
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th January Morning Slot
A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is :
A.
2.0 %
B.
2.5 %
C.
1.0 %
D.
0.5 %
2018 JEE Mains MCQ
JEE Main 2018 (Online) 16th April Morning Slot
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 negligible, the relative uncertainty in the mass of the earth is :
A.
10$-$2
B.
2 $ \times $ 10$-$2
C.
3 $ \times $ 10$-$2
D.
6 $ \times $ 10$-$2
2018 JEE Mains MCQ
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 physical quantity A = ${{{P^3}{Q^2}} \over {\sqrt R S}}.$

The maximum percentage error in the value of A will be :
A.
6.0%
B.
7.5%
C.
8.5%
D.
6.5%
2018 JEE Mains MCQ
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 relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:
A.
6%
B.
2.5%
C.
3.5%
D.
4.5%
2018 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Evening Slot
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c.

Which of the following correctly gives the Planck length ?
A.
G $\hbar $2 c3
B.
G2 $\hbar $ c
C.
${G^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}}{\hbar ^2}c$
D.
${\left( {{{G\hbar } \over {{c^3}}}} \right)^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}}$
2018 JEE Mains MCQ
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 determination of its volume is :
A.
${3 \over 2}\alpha $
B.
${2 \over 3}\alpha $
C.
${5 \over 2}\alpha $
D.
$\alpha $
2018 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Morning Slot
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 divisions. The thickness of a wire measured by this screw gauge gives a reading of $4$ main scale divisions and $30$ circular scale divisions. Assuming negligible zero error, the thickness of the wire is :
A.
$0.4300$ $cm$
B.
$0.2150$ $cm$
C.
$0.3150$ $cm$
D.
$0.0430$ $cm$
2017 JEE Mains MCQ
JEE Main 2017 (Online) 9th April Morning Slot
A physical quantity P is described by the relation

P = a$^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}$ b2 c3 d$-$4

If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be :
A.
8%
B.
12%
C.
32%
D.
25%
2017 JEE Mains MCQ
JEE Main 2017 (Online) 8th April Morning Slot
Time (T), velocity (C) and angular momentum (h) are chosen as fundamentalquantities instead of mass, length and time. In terms of these, the dimensions of mass would be :
A.
[M] = [T$-$1 C$-$2 h]
B.
[M] = [T$-$1 C2 h]
C.
[M] = [T$-$1 C$-$2 h$-$1]
D.
[M] = [T C$-$2 h]
2017 JEE Mains MCQ
JEE Main 2017 (Offline)
The following observations were taken for determining surface tension T of water by capillary method:
diameter of capillary, D = 1.25 $\times$ 10-2 m
rise of water, h = 1.45 $\times$ 10-2m
Using g = 9.80 m/s2 and the simplified relation T = ${{rhg} \over 2} \times {10^3}N/m$, the possible error in surface tension is closest to :
A.
10 %
B.
0.15 %
C.
1.5 %
D.
2.4 %
2016 JEE Mains MCQ
JEE Main 2016 (Online) 9th April Morning Slot
In the following ‘I’ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity :
A.
ML$-$3 T$-$3 I2
B.
M$-$1 L3 T3 I
C.
M$-$1 L$-$3 T3 I2
D.
M$-$1 L$-$3 T3 I
2016 JEE Mains MCQ
JEE Main 2016 (Offline)
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 starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides with the main scale line?
A.
0.70 mm
B.
0.50 mm
C.
0.75 mm
D.
0.80 mm
2016 JEE Mains MCQ
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 and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be :
A.
92 $ \pm $ 1.8 s
B.
92 $ \pm $ 3 s
C.
92 $ \pm $ 2 s
D.
92 $ \pm $ 5.0 s
2016 JEE Mains MSQ
JEE Main 2016 (Online) 10th April Morning Slot
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 = C ln (BD) holds true. Then which of the combination is not a meaningful quantity ?
A.
A2 $-$ B2C2
B.
${{\left( {A - C} \right)} \over D}$
C.
${A \over B} - C$
D.
${C \over {BD}} - {{A{D^2}} \over C}$
2014 JEE Mains MCQ
JEE Main 2014 (Offline)
A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?
A.
A screw gauge having 100 divisions in the circular scale and pitch as 1 mm.
B.
A screw gauge having 50 divisions in the circular scale and pitch as 1 mm.
C.
A meter scale.
D.
A vernier calliper where the 10 divisions in vernier scale matches with 9 division in main scale and main scale has 10 divisions in 1 cm.
2013 JEE Mains MCQ
JEE Main 2013 (Offline)
Let [${\varepsilon _0}$] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:
A.
${\varepsilon _0} = \left[ {{M^{ - 1}}{L^{ - 3}}{T^2}A} \right]$
B.
${\varepsilon _0} = $$\left[ {{M^{ - 1}}{L^{ - 3}}{T^4}{A^2}} \right]$
C.
${\varepsilon _0} = \left[ {{M^1}{L^2}{T^1}{A^2}} \right]$
D.
${\varepsilon _0} = \left[ {{M^1}{L^2}{T^1}A} \right]$
2012 JEE Mains MCQ
AIEEE 2012
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 in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is
A.
6 %
B.
zero
C.
1 %
D.
3 %
2012 JEE Mains MCQ
AIEEE 2012
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 divisions
Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data
A.
58.59 degree
B.
58.77 degree
C.
58.65 degree
D.
59 degree
2011 JEE Mains MCQ
AIEEE 2011
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
Given that 1 mm on main scale corresponds to 100 divisions of the circular scale.
The diameter of wire from the above date is:
A.
0.052 cm
B.
0.026 cm
C.
0.005 cm
D.
0.52 cm
2010 JEE Mains MCQ
AIEEE 2010
The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 $ \times $ 10–3 are
A.
5, 1, 2
B.
5, 1, 5
C.
5, 5, 2
D.
4, 4, 2
2009 JEE Mains MCQ
AIEEE 2009
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 vernier scale. If the smallest division of the main scale is half-a degree(=$0.5^\circ $), then the least count of the instrument is:
A.
one minute
B.
half minute
C.
one degree
D.
half degree
2008 JEE Mains MCQ
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 divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is
A.
3.32 mm
B.
3.73 mm
C.
3.67 mm
D.
3.38 mm
2008 JEE Mains MCQ
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 recorded as
A.
17.6 kg ms-1
B.
17.565 kg ms-1
C.
17.56 kg ms-1
D.
17.57 kg ms-1
2008 JEE Mains MCQ
AIEEE 2008
An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by
A.
a vernier scale provided on the microscope
B.
a standard laboratory scale
C.
a meter scale provided on the microscope
D.
a screw gauge provided on the microscope
2008 JEE Mains MCQ
AIEEE 2008
The dimension of magnetic field in M, L, T and C (coulomb) is given as
A.
MLT-1C-1
B.
MT2C-2
C.
MT-1C-1
D.
MT-2C-1
2005 JEE Mains MCQ
AIEEE 2005
Out of the following pair, which one does NOT have identical dimensions is
A.
angular momentum and Planck's constant
B.
impulse and momentum
C.
moment of inertia and moment of a force
D.
work and torque
2004 JEE Mains MCQ
AIEEE 2004
Which one of the following represents the correct dimensions of the coefficient of viscosity?
A.
ML-1T-1
B.
MLT-1
C.
ML-1T-2
D.
ML-2T-2
2003 JEE Mains MCQ
AIEEE 2003
Dimensions of ${1 \over {{\mu _0}{\varepsilon _0}}}$, where symbols have their usual meaning, are
A.
[ L-1T ]
B.
[ L-2T2 ]
C.
[ L2T-2 ]
D.
[ LT-1 ]
2003 JEE Mains MCQ
AIEEE 2003
The physical quantities not having same dimensions are
A.
torque and work
B.
momentum and Planck's constant
C.
stress and Young's modulus
D.
speed and ${\left( {{\mu _0}{\varepsilon _0}} \right)^{ - 1/2}}$
2002 JEE Mains MCQ
AIEEE 2002
Identify the pair whose dimensions are equal
A.
torque and work
B.
stress and energy
C.
force and stress
D.
force and work