Units & Measurements PYQs - Last 10 Years
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PhysicsMechanics2017-2026
Practice 210 JEE Main Physics questions from Units & Measurements. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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2017-2026
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137 in last 5 years210 in last 10 years
Last 10 Years Units & Measurements Questions
Showing 50 of 210 filtered questions.
1Units And Measurements
The position of a particle moving on $x$-axis is given by $x(t)=A \sin t+B \cos ^2 t+C t^2+D$, where $t$ is time. The dimension of $\frac{A B C}{D}$ is
MCQ+4 / -12025
2Units And Measurements
Match List - I with List - II
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MCQ+4 / -12025
3Units And Measurements
The energy of a system is given as $\mathrm{E}(\mathrm{t})=\alpha^3 \mathrm{e}^{-\beta t}$, where t is the time and $\beta=0.3 \mathrm{~s}^{-1}$. The errors in the measurement of $\alpha$ and $t$ are $1.2 \%$ and $1.6 \%$, respectively. At ...
MCQ+4 / -12025
4Units And Measurements
If $B$ is magnetic field and $\mu_0$ is permeability of free space, then the dimensions of $\left(B / \mu_0\right)$ is
MCQ+4 / -12025
5Units And Measurements
Given below are two statements :
Statement I: In a vernier callipers, one vernier scale division is always smaller than one main scale division.
Statement II : The vernier constant is given by one main scale division multiplied by the numbe...
Statement I: In a vernier callipers, one vernier scale division is always smaller than one main scale division.
Statement II : The vernier constant is given by one main scale division multiplied by the numbe...
MCQ+4 / -12025
6Units And Measurements
The maximum percentage error in the measurment of density of a wire is
[Given, mass of wire $=(0.60 \pm 0.003) \mathrm{g}$
radius of wire $=(0.50 \pm 0.01) \mathrm{cm}$
length of wire $=(10.00 \pm 0.05) \mathrm{cm}]$
[Given, mass of wire $=(0.60 \pm 0.003) \mathrm{g}$
radius of wire $=(0.50 \pm 0.01) \mathrm{cm}$
length of wire $=(10.00 \pm 0.05) \mathrm{cm}]$
MCQ+4 / -12025
7Units And Measurements
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 \((n+1)^{\text {th }}\) division of vernier scale, the least count of the vernier caliper i...
MCQ+4 / -12024
8Units And Measurements
The dimensional formula of latent heat is :
MCQ+4 / -12024
9Units And Measurements
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 constant is :
MCQ+4 / -12024
10Units And Measurements
In an expression \(a \times 10^b\) :
MCQ+4 / -12024
11Units And Measurements
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 division on the main scale is equal to \(1 \mathrm{~mm}\). The main scale reading is $$2 \...
MCQ+4 / -12024
12Units And Measurements
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 the number of divisions of main scale that coincide with \(\mathrm{N}\) divisions of vern...
MCQ+4 / -12024
13Units And Measurements
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 of the circular scale lies 5 divisions below the reference line. The diameter of a wire is ...
MCQ+4 / -12024
14Units And Measurements
If \(\epsilon_{\mathrm{o}}\) is the permittivity of free space and \(\mathrm{E}\) is the electric field, then \(\epsilon_{\mathrm{o}} \mathrm{E}^2\) has the dimensions :
MCQ+4 / -12024
15Units And Measurements
To find the spring constant \((k)\) of a spring experimentally, a student commits \(2 \%\) positive error in the measurement of time and \(1 \%\) negative error in measurement of mass. The percentage error in determining value of \(k\) is :
MCQ+4 / -12024
16Units And Measurements
While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is \(1 \mathrm{~mm}\) and circular scale reading is equal to 42 divisions. Pitch of screw gauge is \(1 \mathrm{~mm}\) and it has 100 di...
MCQ+4 / -12024
17Units And Measurements
Match List I with List II
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MCQ+4 / -12024
18Units And Measurements
In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division \(=49 \mathrm{~MSD} ; 20\) divisions on main scale in each \(\mathrm{cm}\)
For mark on paper
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MCQ+4 / -12024
19Units And Measurements
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 exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 ma...
MCQ+4 / -12024
20Units And Measurements
Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as \(4.62 \mathrm{~s}, 4.632 \mathrm{~s}, 4.6 \mathrm{~s}\) and \(4.64 \mathrm{~s}\). The arithmetic mean of these readings...
MCQ+4 / -12024
21Units And Measurements
A vernier callipers has 20 divisions on the vernier scale, which coincides with \(19^{\text {th }}\) division on the main scale. The least count of the instrument is \(0.1 \mathrm{~mm}\). One main scale division is equal to ________ mm.
MCQ+4 / -12024
22Units And Measurements
What is the dimensional formula of \(a b^{-1}\) in the equation \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where letters have their usual meaning.
MCQ+4 / -12024
23Units And Measurements
The equation of stationary wave is :
\(y=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right) \text {. }\)
Which of the following is NOT correct :
\(y=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right) \text {. }\)
Which of the following is NOT correct :
MCQ+4 / -12024
24Units And Measurements
Applying the principle of homogeneity of dimensions, determine which one is correct,
where \(T\) is time period, \(G\) is gravitational constant, \(M\) is mass, \(r\) is radius of orbit.
where \(T\) is time period, \(G\) is gravitational constant, \(M\) is mass, \(r\) is radius of orbit.
MCQ+4 / -12024
25Units And Measurements
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:
where \(x=\) distance and \(t=\) time. The dimensions of \(b^2 / a\) are:
MCQ+4 / -12024
26Units And Measurements
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 be:
MCQ+4 / -12024
27Units And Measurements
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 measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the...
MCQ+4 / -12024
28Units And Measurements
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, length and time respectively. The dimension of \(A B\) is
MCQ+4 / -12024
29Units And Measurements
Match List I with List II.
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MCQ+4 / -12024
30Units And Measurements
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 $k a$ dimensionless constant)
MCQ+4 / -12024
31Units And Measurements
If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is \(0.5 \mathrm{~mm}\), the Vernier constant of traveling microscope is
MCQ+4 / -12024
32Units And Measurements
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 measurement of \(\mathrm{R}\) is :
MCQ+4 / -12024
33Units And Measurements
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 \(c\) are \(3 \%, 4 \%\) and \(5 \%\) respectively. Then, the percentage error in \(Q\) i...
MCQ+4 / -12024
34Units And Measurements
Given below are two statements :
Statement (I) : Planck's constant and angular momentum have same dimensions.
Statement (II) : Linear momentum and moment of force have same dimensions.
In the light of the above statements, choose the correc...
Statement (I) : Planck's constant and angular momentum have same dimensions.
Statement (II) : Linear momentum and moment of force have same dimensions.
In the light of the above statements, choose the correc...
MCQ+4 / -12024
35Units And Measurements
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 positive zero error exists, then while taking measurements, the reading taken will be more tha...
Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more tha...
MCQ+4 / -12024
36Units And Measurements
The radius $(\mathrm{r})$, length $(l)$ and resistance $(\mathrm{R})$ of a metal wire was measured in the laboratory as
$$
\begin{aligned}
& \mathrm{r}=(0.35 \pm 0.05) ~\mathrm{cm} \\\\
& \mathrm{R}=(100 \pm 10) ~\mathrm{ohm} \\\\
& l=(15 \...
$$
\begin{aligned}
& \mathrm{r}=(0.35 \pm 0.05) ~\mathrm{cm} \\\\
& \mathrm{R}=(100 \pm 10) ~\mathrm{ohm} \\\\
& l=(15 \...
MCQ+4 / -12024
37Units And Measurements
The dimensional formula of angular impulse is :
MCQ+4 / -12024
38Units And Measurements
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 least count of the instrument is :
MCQ+4 / -12024
39Units And Measurements
Match List - I with List - II.
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MCQ+4 / -12024
40Units And Measurements
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 error in its density will be:
MCQ+4 / -12023
41Units And Measurements
Dimension of \(\frac{1}{\mu_{0} \in_{0}}\) should be equal to
MCQ+4 / -12023
42Units And Measurements
Match List I with List II
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MCQ+4 / -12023
43Units And Measurements
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 measurement of equivalent resistance when they are connected in parallel is -
MCQ+4 / -12023
44Units And Measurements
Match List I with List II
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MCQ+4 / -12023
45Units And Measurements
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 circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two...
INTEGER+4 / -12023
46Units And Measurements
Match List I with List II:
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MCQ+4 / -12023
47Units And Measurements
Match List I with List II :
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MCQ+4 / -12023
48Units And Measurements
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 find out the correct dimensions of A and B in a new equation : $${(x - At)^2} + {\left( {y...
MCQ+4 / -12023
49Units And Measurements
Match List I with List II
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MCQ+4 / -12023
50Units And Measurements
Match List I with List II
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MCQ+4 / -12023