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Units and Dimensions

135 Questions Start Allen Test
All Exams Allen Objective Errorless
Q76 Allen ERRORS MCQ
While measuring acceleration due to gravity by a simple pendulum a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of the time period. His percentage error in the measurement of the value of g will be (Use time period of a simple pendulum, $T = 2\pi \sqrt{\frac{\ell}{g}}$ ) -
A.
2 %
B.
4 %
C.
7 %
D.
10 %
Q77 Allen ERRORS MCQ
An experiment measures quantities a, b and c, and X is calculated from $X = ab^{2}/c^{3}$ . If the percentage error in a, b and c are $\pm1\%$ , $\pm3\%$ and $\pm2\%$ respectively, the percentage error in X will be ā€“
A.
$\pm13\%$
B.
$\pm7\%$
C.
$\pm4\%$
D.
$\pm1\%$
Q78 Allen ERRORS MCQ
A physical quantity X is given by $X = \frac{2k^{3}\ell^{2}}{m\sqrt{n}}$ The percentage error in the measurements of k, $\ell$ , m and n are 1%, 1%, 3% and 4% respectively. The value of X is uncertain by
A.
8%
B.
10%
C.
12%
D.
None
Q79 Allen ERRORS MCQ
A quantity is represented by $\mathrm{X} = \mathrm{M}^{\mathrm{a}}\mathrm{L}^{\mathrm{b}}\mathrm{T}^{\mathrm{c}}$ . The percentage error in measurement of M, L and T are $\alpha \%$ , $\beta \%$ and $\gamma \%$ respectively. The percentage error in X would be
A.
$(\alpha a + \beta b + \gamma c) \%$
B.
$(\alpha a - \beta b + \gamma c) \%$
C.
$(\alpha a - \beta b - \gamma c) \%$
D.
None of these
Q80 Allen ERRORS MCQ
the dimensional formula of a physical quantity x is $[M^{-1}L^{3}T^{-2}]$ . The error in measuring the quantities M, L, and T are 2%, 3% and 4%. The maximum percentage of error that occurs in measuring the quantity x is :-
A.
9
B.
10
C.
14
D.
19
Q81 Allen ERRORS MCQ
The pressure P and volume V of a gas are related as $PV^{3/2} = K$ , where K is a constant. The percentage change in the pressure for a decrease of 0.5% in the volume is:
A.
-0.75%
B.
0.75%
C.
1.50%
D.
-1.50%
Q82 Allen MEASUREMENT MCQ
Zero error of an instrument introduces
A.
Systematic errors
B.
Random errors
C.
Both
D.
None of these
Q83 Allen MEASUREMENT MCQ
A pendulum clock, designed to give correct time in planes, gives incorrect time at hill station. Type of error in measurement of time can be :-
A.
Systematic error
B.
Random error
C.
Gross error
D.
None of these
Q84 Allen MEASUREMENT MCQ
A vernier callipers has 40 divisions on the vernier scale which coincide with 38 divisions on the main scale. The least count of the instrument is 0.1 mm. The main scale divisions are of
A.
0.5 mm
B.
1 mm
C.
2 mm
D.
1/4 mm
Q85 Allen MEASUREMENT MCQ
One centimetre on the main scale of vernier callipers is divided into ten equal parts. If 20 divisions of vernier scale coincide with 16 small divisions of the main scale, the least count of the callipers is
A.
0.01 cm
B.
0.02 cm
C.
0.05 cm
D.
0.005 cm
Q86 Allen MEASUREMENT MCQ
In main scale of a vernier callipers 1 cm divided into 10 equal divisions. The vernier scale has 10 equal divisions that correspond to 9 main scale divisions. The measured value by this calliper is :-
A.
$2.82\mathrm{cm}$
B.
$2.83\mathrm{cm}$
C.
$2.87\mathrm{cm}$
D.
$2.89\mathrm{cm}$
Q87 Allen MEASUREMENT MCQ
A student measured the thickness of a metal sheet using a screw gauge with least count 0.001 cm and listed the measurements. The correct measurement is ā€“
A.
4.2 cm
B.
4.22 cm
C.
4.220 cm
D.
4.2200 cm
Q88 Allen MEASUREMENT MCQ
One full rotation of the cap of a screw gauge is equivalent to 5 mm. The cap has 100 division. Find the least count.
A.
0.5 m
B.
0.05 mm
C.
0.005 m
D.
$5 \times 10^{-4}$ m
Q89 Allen MEASUREMENT MCQ
Distance moved by a screw in 5 rotation is 5 mm and total number of circular divisions is 100. The least count of the screw gauge is :
A.
1 mm
B.
0.001 cm
C.
0.0001 cm
D.
0.001 mm
Q90 Allen MEASUREMENT MCQ
The number of circular division on screwgauge is 100. It moves 1 mm on main scale for one complete revolution. Find reading of micrometer.
A.
$3.25 \mathrm{~mm}$
B.
3.24 mm
C.
$3.30 \mathrm{~mm}$
D.
3.41 mm
Q91 Allen MEASUREMENT MCQ
The number of circular division on the shown screw gauge is 100. It moves 1 mm on main scale for one complete rotation and main scale has 1 mm marks. The diameter of the ball is :-
A.
$2.25\mathrm{mm}$
B.
$2.20\mathrm{mm}$
C.
$1.20\mathrm{mm}$
D.
$1.25\mathrm{mm}$
Q92 Allen PYQ MCQ
If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are:
A.
$[F V T^{-1}]$
B.
$[F V T^{-2}]$
C.
$[F V^{-1} T^{-1}]$
D.
$[F V^{-1} T]$
Q93 Allen PYQ MCQ
If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be:
A.
$[EV^{-1}T^{-2}]$
B.
$[EV^{-2}T^{-2}]$
C.
$[E^{-2}V^{-1}T^{-3}]$
D.
$[EV^{-2}T^{-1}]$
Q94 Allen PYQ MCQ
If dimension of critical velocity $v_{C}$ , of liquid flowing through a tube is expressed as $(\eta^{x} \rho^{y} r^{z})$ , where $\eta$ , $\rho$ and r 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:
A.
1, 1, 1
B.
1, -1, -1
C.
-1, -1, 1
D.
-1, -1, -1
Q95 Allen PYQ MCQ
Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?
A.
$\sqrt{\frac{hc}{G}}$
B.
$\sqrt{\frac{Gc}{h^{3/2}}}$
C.
$\frac{\sqrt{hG}}{c^{3/2}}$
D.
$\frac{\sqrt{hG}}{c^{5/2}}$
Q96 Allen PYQ MCQ
A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^{2}}{4\pi\varepsilon_{0}}$ is [c is velocity of light, G is universal constant of gravitation and e is charge] :-
A.
$c^{2}\left[G\frac{e^{2}}{4\pi\varepsilon_{0}}\right]^{1/2}$
B.
$\frac{1}{c^{2}}\left[\frac{e^{2}}{G4\pi\varepsilon_{0}}\right]^{1/2}$
C.
$\frac{1}{c}G\frac{e^{2}}{4\pi\varepsilon_{0}}$
D.
$\frac{1}{c^{2}}\left[G\frac{e^{2}}{4\pi\varepsilon_{0}}\right]^{1/2}$
Q97 Allen PYQ MCQ
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:
A.
0.521 cm
B.
0.525 cm
C.
$0.053 \mathrm{~cm}$
D.
0.529 cm
Q98 Allen PYQ MCQ
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 $X=\frac{A^{2}B^{1/2}}{C^{1/3}D^{3}}$ , will be:
A.
$\left(\frac{3}{13}\right)\%$
B.
16%
C.
-10%
D.
10%
Q99 Allen PYQ MCQ
The unit of thermal conductivity is:
A.
J m K $^{-1}$
B.
J m $^{-1}$ K $^{-1}$
C.
W m K $^{-1}$
D.
W m $^{-1}$ K $^{-1}$
Q100 Allen PYQ MCQ
The main scale of a vernier calliper has n divisions/cm. n divisions of the vernier scale coincide with $(n - 1)$ divisions of main scale. The least count of the vernier calliper is,
A.
$\frac{1}{(n+1)(n-1)}$ cm
B.
$\frac{1}{n}$ cm
C.
$\frac{1}{n^{2}}$ cm
D.
$\frac{1}{n(n+1)}$ cm