question_answer 1)
The period of oscillation of a simple pendulum is given by \[T=2\pi \sqrt{\frac{l}{g}}\]where l is about 100 cm and is known to have 1mm accuracy. The period is about 2s. The time of 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in g is
A)
0.1% done
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B)
1% done
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C)
0.2% done
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D)
0.8% done
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question_answer 2)
The percentage errors in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed
A)
11% done
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B)
8% done
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C)
5% done
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D)
1% done
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question_answer 3)
The random error in the arithmetic mean of 100 observations is x; then random error in the arithmetic mean of 400 observations would be
A)
4x done
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B)
\[\frac{1}{4}x\] done
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C)
2x done
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D)
\[\frac{1}{2}x\] done
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question_answer 4)
What is the number of significant figures in 0.310×103
A)
2 done
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B)
3 done
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C)
4 done
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D)
6 done
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question_answer 5)
Error in the measurement of radius of a sphere is 1%. The error in the calculated value of its volume is [AFMC 2005]
A)
1% done
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B)
3% done
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C)
5% done
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D)
7% done
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question_answer 6)
The mean time period of second's pendulum is 2.00s and mean absolute error in the time period is 0.05s. To express maximum estimate of error, the time period should be written as
A)
(2.00 ± 0.01) s done
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B)
(2.00 +0.025) s done
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C)
(2.00 ± 0.05) s done
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D)
(2.00 ± 0.10) s done
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question_answer 7)
A body travels uniformly a distance of (13.8 ±0.2) m in a time (4.0 ± 0.3) s. The velocity of the body within error limits is
A)
(3.45 ± 0.2) ms-1 done
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B)
(3.45 ± 0.3) ms-1 done
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C)
(3.45 ± 0.4) ms-1 done
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D)
(3.45 ± 0.5) ms-1 done
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question_answer 8)
The percentage error in the above problem is
A)
7% done
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B)
5.95% done
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C)
8.95% done
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D)
9.85% done
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question_answer 9)
The unit of percentage error is
A)
Same as that of physical quantity done
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B)
Different from that of physical quantity done
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C)
Percentage error is unit less done
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D)
Errors have got their own units which are different from that of physical quantity measured done
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question_answer 10)
The decimal equivalent of 1/20 upto three significant figures is
A)
0.0500 done
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B)
0.05000 done
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C)
0.0050 done
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D)
5.0 × 10-2 done
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question_answer 11)
Accuracy of measurement is determined by
A)
Absolute error done
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B)
Percentage error done
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C)
Both done
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D)
None of these done
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question_answer 12)
The radius of a sphere is (5.3 ± 0.1) cm. The percentage error in its volume is
A)
\[\frac{0.1}{5.3}\times 100\] done
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B)
\[3\times \frac{0.1}{5.3}\times 100\] done
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C)
\[\frac{0.1\times 100}{3.53}\] done
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D)
\[3+\frac{0.1}{5.3}\times 100\] done
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question_answer 13)
A thin copper wire of length l metre increases in length by 2% when heated through 10ºC. What is the percentage increase in area when a square copper sheet of lengthlmetre is heated through 10ºC
A)
4% done
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B)
8% done
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C)
16% done
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D)
None of the above done
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question_answer 14)
In the context of accuracy of measurement and significant figures in expressing results of experiment, which of the following is/are correct
A)
(1) Out of the two measurements 50.14 cm and 0.00025 ampere, the first one has greater accuracy (2) If one travels 478 km by rail and 397 m. by road, the total distance travelled is 478 km. Only (1) is correct done
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B)
Only (2) is correct done
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C)
Both are correct done
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D)
None of them is correct. done
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question_answer 15)
A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation a = \[{{b}^{\alpha }}{{c}^{\beta }}/{{d}^{\gamma }}{{e}^{\delta }}\]. If the maximum errors in the measurement of b, c, d and e are \[{{b}_{1}}\]%, \[{{c}_{1}}\]%, \[{{d}_{1}}\]% and \[{{e}_{1}}\]%, then the maximum error in the value of a determined by the experiment is
A)
(\[{{b}_{1}}\,+\,{{c}_{1}}\,+\,{{d}_{1}}\,+\,{{e}_{1}}\])% done
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B)
(\[{{b}_{1\,}}\,+\,{{c}_{1}}\,-\,{{d}_{1}}\,-\,{{e}_{1}}\])% done
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C)
(\[\alpha {{b}_{1}}\,+\,\beta {{c}_{1}}\,-\,\gamma {{d}_{1}}\,-\delta {{e}_{1}}\])% done
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D)
(\[\alpha {{b}_{1}}+\,\beta {{c}_{1}}\,+\,\gamma {{d}_{1}}\,+\,\delta {{e}_{1}}\])% done
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question_answer 16)
The relative density of material of a body is found by weighing it first in air and then in water. If the weight in air is (5.00\[\pm 0.05\]) Newton and weight in water is (4.00\[\pm \]0.05) Newton. Then the relative density along with the maximum permissible percentage error is
A)
5.0 \[\pm \]11% done
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B)
5.0 \[\pm \]1% done
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C)
5.0 \[\pm \]6% done
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D)
1.25 \[\pm \]5% done
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question_answer 17)
The resistance R =\[\frac{V}{i}\] where V= 100 \[\pm \]5 volts and i = 10 \[\pm \]0.2 amperes. What is the total error in R
A)
5% done
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B)
7% done
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C)
5.2% done
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D)
\[\frac{5}{2}\]% done
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question_answer 18)
The period of oscillation of a simple pendulum in the experiment is recorded as 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s respectively. The average absolute error is
A)
0.1 s done
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B)
0.11 s done
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C)
0.01 s done
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D)
1.0 s done
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question_answer 19)
The length of a cylinder is measured with a meter rod having least count 0.1 cm. Its diameter is measured with vernier calipers having least count 0.01 cm. Given that length is 5.0 cm. and radius is 2.0 cm. The percentage error in the calculated value of the volume will be
A)
1% done
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B)
2% done
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C)
3% done
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D)
4% done
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question_answer 20)
In an experiment, the following observation's were recorded : L = 2.820 m, M = 3.00 kg, l = 0.087 cm, Diameter D = 0.041 cm Taking g = 9.81 \[m/{{s}^{2}}\]using the formula , Y=\[\frac{4MgL}{\pi {{D}^{2}}l}\], the maximum permissible error in Y is
A)
7.96% done
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B)
4.56% done
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C)
6.50% done
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D)
8.42% done
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question_answer 21)
According to Joule's law of heating, heat produced \[H={{I}^{2}}\]Rt, where I is current, R is resistance and t is time. If the errors in the measurement of I, R and t are 3%, 4% and 6% respectively then error in the measurement of H is
A)
\[\pm \]17% done
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B)
\[\pm \]16% done
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C)
\[\pm \]19% done
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D)
\[\pm \]25% done
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question_answer 22)
If there is a positive error of 50% in the measurement of velocity of a body, then the error in the measurement of kinetic energy is
A)
25% done
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B)
50% done
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C)
100% done
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D)
125% done
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question_answer 23)
A physical quantity P is given by P=\[\frac{{{A}^{3}}{{B}^{\frac{1}{2}}}}{{{C}^{-4}}{{D}^{\frac{3}{2}}}}\]. The quantity which brings in the maximum percentage error in P is
A)
A done
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B)
B done
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C)
C done
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D)
D done
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question_answer 24)
If \[L=2.331\,cm,\ B=2.1\,cm\], then \[L+B=\] [DCE 2003]
A)
4.431 cm done
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B)
4.43 cm done
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C)
4.4 cm done
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D)
4 cm done
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question_answer 25)
The number of significant figures in all the given numbers 25.12, 2009, 4.156 and \[1.217\times {{10}^{-4}}\] is [Pb. PET 2003]
A)
1 done
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B)
2 done
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C)
3 done
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D)
4 done
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question_answer 26)
If the length of rod A is 3.25 ± 0.01 cm and that of B is 4.19 ± 0.01 cm then the rod B is longer than rod A by [J&K CET 2005]
A)
0.94 ± 0.00 cm done
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B)
0.94 ± 0.01 cm done
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C)
0.94 ± 0.02 cm done
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D)
0.94 ± 0.005 cm done
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question_answer 27)
A physical quantity is given by \[X={{M}^{a}}{{L}^{b}}{{T}^{c}}\]. The percentage error in measurement of \[M,L\]and T are \[\alpha ,\beta \]and \[\gamma \] respectively. Then maximum percentage error in the quantity X is [Orissa JEE 2005]
A)
\[a\alpha +b\beta +c\gamma \] done
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B)
\[a\alpha +b\beta -c\gamma \] done
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C)
\[\frac{a}{\alpha }+\frac{b}{\beta }+\frac{c}{\gamma }\] done
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D)
None of these done
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question_answer 28)
A physical quantity A is related to four observable \[a,b,c\] and d as follows, \[A=\frac{{{a}^{2}}{{b}^{3}}}{c\sqrt{d}}\], the percentage errors of measurement in \[a,b,c\] and d are 1%,3%,2% and 2% respectively. What is the percentage error in the quantity A [Kerala PET 2005]
A)
12% done
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B)
7% done
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C)
5% done
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D)
14% done
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