Q.No:1 CSIR Dec-2014
In a measurement of the viscous drag force experienced by spherical particles in a liquid, the force is found to be proportional to \(V^{1/3}\) where \(V\) is the measured volume of each particle. If \(V\) is measured to be \(30 mm^3\), with an uncertainty of \(2.7 mm^3\), the resulting relative percentage uncertainty in the measured force is
(1)
\(2.08\)
(2)
\(0.09\)
(3)
\(6\)
(4)
\(3\)
Check Answer
Option 4
Q.No:2 CSIR Jun-2015
The viscosity \( \eta \) of a liquid is given by Poiseuille's formula
\[
\eta = \frac{\pi P a^4}{8 l V}
\]
Assume that \( l \) and \( V \) can be measured very accurately, but the pressure \( P \) has an rms error of \( 1\% \) and the radius \( a \) has an independent rms error of \( 3\% \). The rms error of the viscosity is closest to
(1)
\(2\%\)
(2)
\(4\%\)
(3)
\(12\%\)
(4)
\(13\%\)
Check Answer
Option 3
Q.No:3 CSIR Jun-2016
The decay constants \(f_p\) of the heavy pseudo-scalar mesons, in the heavy quark limit, are related to their masses \(m_p\) by the relation \(f_p=\frac{a}{\sqrt{m_p}}\), where \(a\) is an empirical parameter to be determined. The values \(m_p=6400\pm 160 MeV\) and \(f_p=180\pm 15 MeV\) correspond to uncorrelated measurements of a meson. The error on the estimate of \(a\) is
(1)
\(175 (MeV)^{3/2}\)
(2)
\(900 (MeV)^{3/2}\)
(3)
\(1200 (MeV)^{3/2}\)
(4)
\(2400 (MeV)^{3/2}\)
Check Answer
Option 3
Q.No:4 CSIR Jun-2017
The experimentally measured values of the variables \(x\) and \(y\) are \(2.00\pm 0.05\) and \(3.00\pm 0.02\), respectively. What is the error in the calculated value of \(z=3y-2x\) from the measurements?
(1)
\(0.12\)
(2)
\(0.05\)
(3)
\(0.03\)
(4)
\(0.07\)
Check Answer
Option 1
Q.No:5 CSIR Jun-2017
Both the data points and a linear fit to the current vs voltage of a resistor are shown in the graph below.
If the error in the slope is \(1.255 \times 10^{-3} \Omega^{-1}\), then the value of resistance estimated from the graph is
(1)
\((0.04\pm 0.8) \Omega\)
(2)
\((25.0\pm 0.8) \Omega\)
(3)
\((25\pm 1.25) \Omega\)
(4)
\((25\pm 0.0125) \Omega\)
Check Answer
Option 2
Q.No:6 CSIR Dec-2017
Two physical quantities \(T\) and \(M\) are related by the equation \(T=\frac{2\pi}{a}\sqrt{\frac{M+b}{2}}\), where \(a\) and \(b\) are constant parameters. The variation of \(T\) as a function of \(M\) was recorded in an experiment to determine the value of \(a\) graphically. Let \(m\) be the slope of the straight line when \(T^2\) is plotted vs \(M\), and \(\delta m\) be the uncertainty in determining it. The uncertainty in determining \(a\) is
(1)
\(\frac{a}{2}\left(\frac{\delta m}{m}\right)\)
(2)
\(a\left(\frac{\delta m}{m}\right)\)
(3)
\(\frac{b}{2a}\left(\frac{\delta m}{m}\right)\)
(4)
\(\frac{2\pi}{a}\left(\frac{\delta m}{m}\right)\)
Check Answer
Option 1
Q.No:7 CSIR Jun-2019
In an experiment to measure the acceleration due to gravity \(g\) using a simple pendulum, the length and time period of the pendulum are measured to three significant figures. The mean value of \(g\) and the uncertainty \(\delta g\) of the measurements are then estimated using a calculator from a large number of measurements and found to be \(9.82147 m/s^2\) and \(0.02357 m/s^2\), respectively. Which of the following is the most accurate way of presenting the experimentally determined value of \(g\)?
(1)
\(9.82\pm 0.02 m/s^2\)
(2)
\(9.8215\pm 0.02 m/s^2\)
(3)
\(9.82147\pm 0.02357 m/s^2\)
(4)
\(9.82\pm 0.02357 m/s^2\)
Check Answer
Option 1
Q.No:8 CSIR Dec-2019
A student measures the displacement \(x\) from the equilibrium of a stretched spring and reports it be \(100 \mu m\) with a \(1\%\) error. The spring constant \(k\) is known to be \(10 N/m\) with \(0.5\%\) error. The percentage error in the estimate of the potential energy \(V=\frac{1}{2}kx^2\) is
(1)
\(0.8\%\)
(2)
\(2.5\%\)
(3)
\(1.5\%\)
(4)
\(3.0\%\)
Check Answer
Option 2
Q.No:9 CSIR Assam Dec-2019
In order to determine the volume of a solid cylinder, its radius \(r\) and height \(h\) were measured. The measured values of the radius and height were found to be in the ranges \(1.9 cm\leq r\leq 2.1 cm\) and \(9.9 cm\leq h\leq 10.1 cm\), respectively. The range of values for the calculated volume of the cylinder is
(1)
\(35.7\pi cm^3\leq V\leq 44.5\pi cm^3\)
(2)
\(34.5\pi cm^3\leq V\leq 44.1\pi cm^3\)
(3)
\(34.8\pi cm^3\leq V\leq 45.7\pi cm^3\)
(4)
\(39.7\pi cm^3\leq V\leq 46.4\pi cm^3\)
Check Answer
Option 1
Q.No:10 CSIR Feb-2022
In an experiment, the velocity of a non-relativistic neutron is determined by measuring the
time (~ 50 ns) it takes to travel from the source to the detector kept at a distance \(L\). Assume that
the error in the measurement of \(L\) is negligibly small. If we want to estimate the kinetic energy
\(T\) of the neutron to within \(5\%\) accuracy, i.e., \(|\delta T/T|\leq 0.05\) , the maximum permissible error
\(|\delta T|\) in measuring the time of flight is nearest to
(1)
\(1.75\) ns
(2)
\(0.75\) ns
(3)
\(2.25\) ns
(4)
\(1.25\) ns
Check Answer
Option 4
Q.No:11 CSIR Sep-2022
Four students (\(S_1,S_2,S_3\) and \(S_4\)) make multiple measurements on the length of a table. The binned data are plotted as histograms in the following figures.
If the length of the table, specified by a manufacture, is 3m, the students whose measurements have the minimum systematic error, is
(1)
\(S_2\)
(2)
\(S_1\)
(3)
\(S_4\)
(4)
\(S_3\)
Check Answer
Option 2
Q.No:12 CSIR June-2023
A DC motor is used to lift a mass \(M\) to a height \(h\) from the ground. The electric energy delivered to the motor is \(VIt\) , where \(V\) is the applied voltage, \(I\) is the current and \(t\) the time for which the motor runs. The efficiency \(e\) of the motor is the ratio between the work done by the motor and the energy delivered to it. If \(M=2.00\pm0.02 \hspace{1mm}kg\), \(h=1.00\pm0.01 \hspace{1mm}m\), \(V=10.0\pm0.1 \hspace{1mm}V\), \(I=2.00\pm0.02 \hspace{1mm}A\) and \(t=300\pm15 \hspace{1mm}s\), then the fractional error \(|\delta e/e|\) in the efficiency of the motor is closest to
1) 0.05
2) 0.09
3) 0.12
4) 0.15
Check Answer
Option 1
Q.No:13 CSIR Dce-2023
In the measurement of a radioactive sample, the measured counts with and without the sample for equal time intervals are \( C = 500 \) and \( B = 100 \), respectively. The errors in the measurements of \( C \) and \( B \) are \( |\Delta C| = 20 \) and \( |\Delta B| = 10 \), respectively. The net error \( |\Delta Y| \) in the measured counts from the sample \( Y = C - B \), is closest to
1) 22
2)10
3) 30
4) 43
Check Answer
Option 1
Q.No:14 CSIR June -2024
A set of 100 data points yields an average \(\bar{x} = 9\) and a standard deviation \(\sigma_x = 4\). The error in the estimated mean is closest to
1) 3.0
2) 0.4
3) 4.0
4) 0.3
Check Answer
Option 2
Q.No:15 CSIR Dec-2024
The following table shows the relationship between an independent quantity \(x\)
and an experimentally measured quantity \(y\).
\[
\begin{array}{c|cccccc}
x & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline
y & 0.1 & 2.1 & 8.1 & 17.9 & 32.2 & 49.7
\end{array}
\]
The relationship between \(x\) and \(y\) is best represented by
1) \(y \propto x^3\)
2) \(y \propto e^x\)
3) \(y \propto x^2\)
4) \(y \propto \sqrt{x}\)
Check Answer
Option 3
Q.No:16 CSIR Dec-2024
A DC motor operating at a voltage \(V\) and a current \(I\) is used to lift a mass
\(m\) to a height \(h\) in time \(t\).
The percentage uncertainty in the measurement of time \(t\) is \(5\%\), and that
for the other parameters \((V, I, m, h)\) are \(1\%\) each. If the measurements
are independent and the errors are random, the uncertainty in the estimation of
the efficiency
\(
(\frac{\text{output power}}{\text{input power}}
)\)
of the motor is closest to
1) \(3.1\%\)
2) \(5.4\%\)
3) \(4.8\%\)
4) \(6.3\%\)
Check Answer
Option 2
Q.No:1 JEST-2012
The length and radius of a perfect cylinder are each measured with an RMS error of \(1\%\). The RMS error on the inferred volume of the cylinder is roughly
(a)
\(1.7\%\)
(b)
\(3.3\%\)
(c)
\(0.5\%\)
(d)
\(1\%\)
Check Answer
Option a
Q.No:2 JEST-2014
The formula for normal strain in a longitudinal bar is given by \(\varepsilon=\frac{F}{AE}\), where \(F\) is normal force applied, \(A\) is cross-sectional area of the bar and \(E\) is Young's modulus. If \(F=50\pm 0.5 N, A=0.2\pm 0.002 m^2\) and \(E=210\times 10^9\pm 1\times 10^9 Pa\), the maximum error in the measurement of strain is
(a)
\(1.0\times 10^{-12}\)
(b)
\(2.95\times 10^{-11}\)
(c)
\(1.2\times 10^{-9}\)
(d)
\(1.19\times 10^{-9}\)
Check Answer
Option b
Q.No:3 JEST-2015
In Millikan's oil drop experiment the electronic charge \(e\) could be written as \(k\eta^{1.5}\), where \(\kappa\) is a function of all experimental parameters with negligible error. If the viscosity of air \(\eta\) is taken to be \(0.4\%\) lower than the actual value, what would be the error in the calculated value of \(e\)?
(a)
\(1.5\%\)
(b)
\(0.7\%\)
(c)
\(0.6\%\)
(d)
\(0.4\%\)
Check Answer
Option d
Q.No:4 JEST-2021
An astrophysical observation measured the mass of a star as \((12.41\pm 1.12)M_{\odot}\), where \(M_{\odot}\) is the mass of the Sun. Another independent observation measured the mass of the same star as \((8.40\pm \Delta)M_{\odot}\). Assuming the errors to have Gaussian distributions, one concluded that the two measurements differed by \(3\) standard deviations. The value of \(\Delta\) was approximately
(a)
\(0.22\)
(b)
\(0.73\)
(c)
\(1.04\)
(d)
\(1.55\)
Check Answer
Option b
Q.No:5 JEST-2025
A slide calipers instrument has the smallest main scale division of
\(0.4\ \text{mm}\), and 40 vernier divisions match with 38 main scale divisions.
The vernier constant of this instrument is
a) \(0.01\ \text{mm}\)
b) \(0.1\ \text{mm}\)
c) \(0.02\ \text{mm}\)
d) \(0.05\ \text{mm}\)
Check Answer
Option c
Q.No:1 TIFR-2017
A liquid is flowing through a capillary tube of inner radius \(r\) under the influence of an external pressure \(P\). The uncertainties in the measurements of \(P\) and \(r\) are found to be \(2\%\) and \(1\%\), respectively. The uncertainty in the flow of liquid per second is
(a)
\(4.47\%\)
(b)
\(2.23\%\)
(c)
\(2.83\%\)
(d)
\(3.61\%\)
Check Answer
Option a
Q.No:2 TIFR-2021
In an experiment that measures the resistivity \(\rho\) of a substance it was observed that \(\rho\) varies with temperature \(T\) and a parameter \(\Delta\), as
\[
\rho=\rho_0 e^{\Delta/T}
\]
where \(\rho_0\) is a constant.
In one measurement, made at \(T=100 \hspace{1mm}\text{K}\) and \(\Delta=50\), the percentage error in \(\Delta\) is found to be \(2\%\) while the percentage error in \(T\) was \(3\%\). What was the approximate percentage error for the resistivity \(\rho\)?
(a)
\(1.8\%\)
(b)
\(3.6\%\)
(c)
\(9\%\)
(d)
\(18\%\)
Check Answer
Option a
Q.No:3 TIFR-2021
A very sensitive spring balance with spring constant \(k=2\times 10^8 \hspace{1mm}\text{N}\text{m}^{-1}\) is operating at a temperature of \(300 \hspace{1mm}\text{K}\). The thermal fluctuations can lead to an error in the measurement of mass. If you are trying to measure a mass of \(1 \hspace{1mm}\text{mg}\), the relative error in the measurement is closest to
(a)
\(0.9\%\)
(b)
\(10.0\%\)
(c)
\(20.0\%\)
(d)
\(0.01\%\)
Check Answer
Option a
Q.No:4 TIFR-2022
Two students A and B, measure the time period of a simple pendulum in the laboratory using the same stopwatch but following two different methods.
--- Student A measures the time taken for one oscillation and repeats it for \(N_A\) number of times and finds the average.
--- Student B, on the other hand, measures the time taken for \(N_B\) number of oscillations and then computes the period.
Given that \(N_A, N_B \gg 1\), to ensure that both students measure the time period with the same uncertainty, the relation between \(N_A\) and \(N_B\) must be
(a)
\(N_A= N_B ^2\)
(b)
\(N_A= \sqrt{N_B}\)
(c)
\(N_A= N_B \)
(d)
\(ln \hspace{1mm} 2 \hspace{1mm} N_A= N_B\)
Check Answer
Option a
Q.No:5 TIFR-2022
A spectrographic method to search for exoplanets is by measuring its velocity along the line of sight, using the Doppler shift in the spectrum. If a star of mass \(M\) and a planet of mass \(m\) are moving around their common centre of mass, this component of velocity will vary periodically with an amplitude.
\[A=(\frac{2 \pi G_N}{T})^{1/3} \hspace{1mm} \frac{m}{M^{2/3}}\]
For a particular planet-star system, if the time period is \(T=(12 \pm 0.3)\) years, and \(A\) and \(M\) are measured with an accuracy of \(3\%\) each, then the error in the measurement of the mass \(m\) is
(a)
\(3.7\%\)
(b)
\(8.5\%\)
(c)
\(5.8\%\)
(d)
\(6.3\%\)
Check Answer
Option a
Q.No:6 TIFR-2025
For a given measurement of particles in a counter, a 10-minute data collection
resulted in a statistical uncertainty of \(2.5\%\).
How much additional time must be allocated to reduce the statistical
uncertainty to \(0.5\%\)?
a) 240 minutes
b) 40 minutes
c) 250 minutes
d) 50 minutes