Q. No.A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field \(\overrightarrow{{E}}_1={E}_0 \hat{x} .\) If another electric field \(\overrightarrow{{E}}_2=2 {E}_0(\hat{y}+\hat{z})\) is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?
1. \(73\%\)
2. \(63\%\)
3. \(83\%\)
4. \(53\%\)
1. \(73\%\)
2. \(63\%\)
3. \(83\%\)
4. \(53\%\)
Subtopic: Errors |
59%
Level 3: 35%-60%
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The percentage error in the calculated volume of a sphere, if there is \(2\%\) error in its diameter measurement, is:
1. \(1\)
2. \(2\)
3. \(6\)
4. \(8\)
1. \(1\)
2. \(2\)
3. \(6\)
4. \(8\)
Subtopic: Errors |
90%
Level 1: 80%+
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The density \(\rho\) of a uniform cylinder is determined by measuring its mass \(m,\) length \(l\) and diameter \(d.\) The measured values of \(m,l\) and \(d\) are \(97.42 \pm 0.02 ~\text{g},\) \(8.35 \pm 0.05 ~\text{mm} \text { and } 20.20 \pm 0.02 ~\text{mm} \text {,}\) respectively. Calculated percentage fractional error in \(\rho\) is:
1. \(0.63\%\)
2. \(0.82\%\)
3. \(0.72\%\)
4. \(0.25\%\)
1. \(0.63\%\)
2. \(0.82\%\)
3. \(0.72\%\)
4. \(0.25\%\)
Subtopic: Errors |
62%
Level 2: 60%+
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The increase in the pressure required to decrease the volume \((\Delta V)\) of water is \(6.3 \times 10^7~\text{N/m}^2\). The percentage decrease in the volume is:
(Bulk modulus of water \(=2.1 \times 10^9 ~\text{N/m}^2\).)
1. \(2 \%\)
2. \(3 \%\)
3. \(6 \%\)
4. \(4 \%\)
(Bulk modulus of water \(=2.1 \times 10^9 ~\text{N/m}^2\).)
1. \(2 \%\)
2. \(3 \%\)
3. \(6 \%\)
4. \(4 \%\)
Subtopic: Errors |
89%
Level 1: 80%+
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In an experiment the values of two spring constants were measured as \({k}_1=(10 \pm 0.2) ~\text{N/m}\) and \({k}_2=(20 \pm 0.3) ~\text{N/m}.\) If these springs are connected in parallel, then the percentage error in equivalent spring constant is:
1. \(2.67\%\)
2. \(2.33\%\)
3. \(1.33\%\)
4. \(1.67\%\)
1. \(2.67\%\)
2. \(2.33\%\)
3. \(1.33\%\)
4. \(1.67\%\)
Subtopic: Errors |
84%
Level 1: 80%+
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When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height \(h\). If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by \(1\%\) each, then the height of the liquid in the tube will change by (in \(\%\))
1. \(-1\)
2. \(+3\)
3. \(-3\)
4. \(+1\)
1. \(-1\)
2. \(+3\)
3. \(-3\)
4. \(+1\)
Subtopic: Errors |
63%
Level 2: 60%+
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Four persons measure the length of a rod as \(20.00\) cm, \(19.75\) cm, \(17.01\) cm and \(18.25\) cm.
The relative error in the measurement of average length of the rod is:
1. \(0.24\)
2. \(0.18\)
3. \(0.06\)
4. \(0.08\)
The relative error in the measurement of average length of the rod is:
1. \(0.24\)
2. \(0.18\)
3. \(0.06\)
4. \(0.08\)
Subtopic: Errors |
83%
Level 1: 80%+
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The time period of a simple harmonic oscillator is \(T= 2 \pi \sqrt {\dfrac{k}{m}} \). The measured value of mass \((m)\) of the object is \(10~\text{g}\) with an accuracy of \(10~\text{mg}\), and time for \(50\) oscillations of the spring is found to be \(60~\text{s}\) using a watch of \(2~\text{s}\) resolution. Percentage error in determination of spring constant \((k)\) is: (in \(\%\))
1. \(3.43\)
2. \(3.35\)
3. \(7.60\)
4. \(6.76\)
1. \(3.43\)
2. \(3.35\)
3. \(7.60\)
4. \(6.76\)
Subtopic: Errors |
83%
Level 1: 80%+
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A physical quantity \(C\) is related to four other quantities \(p, q, r\) and \(s\) as follows
\(C=\dfrac{{pq}^2}{{r}^2\sqrt s}\)
The percentage errors in the measurement of \(p, q, r\) and \(s\) are \(1\%, 2\%, 3\%\) and \(2\%,\) respectively. The percentage error in the measurement of \(C\) will be: (in \(\%\))
1. \(10\)
2. \(16\)
3. \(12\)
4. \(30\)
\(C=\dfrac{{pq}^2}{{r}^2\sqrt s}\)
The percentage errors in the measurement of \(p, q, r\) and \(s\) are \(1\%, 2\%, 3\%\) and \(2\%,\) respectively. The percentage error in the measurement of \(C\) will be: (in \(\%\))
1. \(10\)
2. \(16\)
3. \(12\)
4. \(30\)
Subtopic: Errors |
92%
Level 1: 80%+
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A quantity \(Q\) is formulated as \(X^{-2} Y^{+{3}/{2}} Z^{-{2}/{5}} . \) \({X}\) and \(Z\) are independent parameters which have fractional errors of \(0.1, 0.2 \) and \(0.5\) respectively in measurement. The maximum fractional error of \(Q \) is:
1. \(0.1\)
2. \(0.8\)
3. \(0.7\)
4. \(0.6\)
1. \(0.1\)
2. \(0.8\)
3. \(0.7\)
4. \(0.6\)
Subtopic: Errors |
85%
Level 1: 80%+
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