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Units and Dimensions

135 Questions Start Allen Test
All Exams Allen Objective Errorless
Q51 Allen DIMENSIONS MCQ
A system has basic dimensions as density [D], velocity [V] and area [A]. The dimensional representation of force in this system is:
A.
$\mathrm{AV}^2\mathrm{D}$
B.
$\mathrm{A}^2\mathrm{VD}$
C.
$\mathrm{AVD}^2$
D.
$\mathrm{A}^0\mathrm{VD}$
Q52 Allen ERRORS MCQ
The significant digits in 200.40 are :-
A.
4
B.
5
C.
2
D.
3
Q53 Allen ERRORS MCQ
Number of significant digits in 0.01230 is :-
A.
3
B.
4
C.
5
D.
6
Q54 Allen ERRORS MCQ
Which of the following has the highest number of significant figures?
A.
$0.007 \, m^{2}$
B.
$2.64 \times 10^{24} \, kg$
C.
$0.0006032 \, m^{2}$
D.
6.3200 J
Q55 Allen ERRORS MCQ
Given P = 0.0030 m, Q = 2.40 m and R = 3000m, the number of significant figures in P, Q and R are respectively :-
A.
1, 2, 1
B.
2, 3, 4
C.
4, 2, 1
D.
4, 2, 4
Q56 Allen ERRORS MCQ
After rounding off the number 4621 to 2 significant digits the value becomes :-
A.
4600
B.
4500
C.
4700
D.
4720
Q57 Allen ERRORS MCQ
If L = 2.331 cm and B = 2.1 cm, then L + B = (According to significant figures)
A.
4.431 cm
B.
4.43 cm
C.
4.4 cm
D.
4 cm
Q58 Allen ERRORS MCQ
Subtract 0.2 J from 5.27 J and express the result with correct number of significant figures :-
A.
5.1 J
B.
5.06 J
C.
5.0 J
D.
5 J
Q59 Allen ERRORS MCQ
In arithmetic $17.8 \times 3.1143 = 55.4354$ . But as a result of experimental measurements the best way to express the product is:
A.
55.3454
B.
55.4
C.
55.44
D.
55.435
Q60 Allen ERRORS MCQ
The order of magnitude of the number 1013 is:-
A.
1
B.
2
C.
3
D.
4
Q61 Allen ERRORS MCQ
The length of a rod is $(11.05 \pm 0.05)$ cm. What is the sum of lengths of two such rods:
A.
$(22.1 \pm 0.05)$ cm
B.
$(22.10 \pm 0.05)$ cm
C.
$(22.1 \pm 0.15)$ cm
D.
$(22.10 \pm 0.10)$ cm
Q62 Allen ERRORS MCQ
The external and internal radius of a hollow cylinder are measured to be $(5.23 \pm 0.015)$ cm and $(4.89 \pm 0.005)$ cm. The thickness of the wall of the cylinder is :-
A.
$(0.34 \pm 0.02)$ cm
B.
$(0.17 \pm 0.02)$ cm
C.
$(0.17 \pm 0.01)$ cm
D.
$(0.34 \pm 0.01)$ cm
Q63 Allen ERRORS MCQ
The resistance is $R = \frac{V}{I}$ where $V = (100 \pm 5)$ volt and $I = (10 \pm 0.2)$ ampere. What is the total error in R?
A.
5 %
B.
7 %
C.
5.2 %
D.
$\left(\frac{5}{2}\right)\%$
Q64 Allen ERRORS MCQ
When a copper sphere is heated, maximum percentage change will be observed in-
A.
radius
B.
area
C.
volume
D.
none of these
Q65 Allen ERRORS MCQ
If error in measuring diameter of a circle is 2%, the error in circumference of the circle would be :-
A.
2%
B.
8%
C.
4%
D.
1%
Q66 Allen ERRORS MCQ
The error is the measurement of volume of sphere is 1.5%. The error in the measurement of its diameter is :-
A.
1%
B.
2%
C.
0.5%
D.
1.5%
Q67 Allen ERRORS MCQ
There is an error of 2% in the measurement of side of a cube. The percentage error in the calculation of its volume will be :-
A.
1%
B.
2%
C.
3
D.
6%
Q68 Allen ERRORS MCQ
A thin copper wire of length $\ell$ metre increases in length by 2% when heated through 10°C. What is the percentage increase in area when a square copper sheet of length $\ell$ metre is heated through 10°C?
A.
4%
B.
8%
C.
16%
D.
None of these
Q69 Allen ERRORS MCQ
If $f = x^2$ , then the relative error in $f$ is:
A.
$\frac{2\Delta x}{x}$
B.
$\frac{(\Delta x)^2}{x}$
C.
$\frac{\Delta x}{x}$
D.
$(\Delta x)^2$
Q70 Allen ERRORS MCQ
The percentage error in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimate of kinetic energy obtained by measuring mass and speed :-
A.
11%
B.
8%
C.
5%
D.
4%
Q71 Allen ERRORS MCQ
The heat generated in a circuit is dependent upon the resistance, current and time for which the current is flown. If the error in measuring the above are as 1%, 2% and 1% the maximum error in measuring heat will be
A.
2%
B.
3%
C.
6%
D.
1%
Q72 Allen ERRORS MCQ
Percentage error in measuring the radius (R) and mass (M) of a solid sphere are 2% & 1% respectively. Then error in measurement of moment of inertia about to its diameter (i.e. I = $\frac{2}{5}$ MR $^2$ ) is :-
A.
3 %
B.
6 %
C.
5 %
D.
4 %
Q73 Allen ERRORS MCQ
The resistance R of a wire is given by the relation $R = \frac{\rho\ell}{\pi r^{2}}$ . Percentage error in the measurement of $\rho$ , $\ell$ and r is 1%, 3% and 2% respectively. Then the percentage error in the measurement of R is
A.
6%
B.
9%
C.
8%
D.
10%
Q74 Allen ERRORS MCQ
The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, the maximum error in the measurement of pressure is –
A.
1%
B.
2%
C.
6%
D.
8%
Q75 Allen ERRORS MCQ
What is the fractional error in g calculated from $T=2\pi\sqrt{\ell/g}$ ? Given that fractional errors in T and $\ell$ are $\pm x$ and $\pm y$ respectively.
A.
$x + y$
B.
x - y
C.
$2x + y$
D.
2x - y