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Q. No.
The estimate of absolute error in the measurement of time using a clock is \(10^{-2}~\text{s}.\) The time difference, \(t=t_1-t_2,\) between two events is determined by using the clock. The error in \(t\) is:
1. \(10^{-2}~\text{s}\)
2. \(2\times10^{-2}~\text{s}\)
3. \(\dfrac{1}{2}\times10^{-2}~\text{s}\)
4. zero
Subtopic:  Errors |
 55%
Level 3: 35%-60%

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Suppose that the value of Newton's gravitational constant is determined from the equation; \(F=G{\Large\frac{m_1m_2}{r^2}},\) by a taking direct measurement of the quantities. The relative errors in the measurements are: force, \(F\rightarrow2\%,\) masses \((m_1,m_2)\rightarrow1\%\) and separation \((r)\rightarrow1\%.\) The relative error in the measurement of \(G\) will be:
1. \(2\%\) 2. \(4\%\)
3. \(6\%\) 4. \(8\%\)
Subtopic:  Errors |
 72%
Level 2: 60%+

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The value of Stefan's constant \((\sigma)\) is determined by experimentally measuring the remaining quantities in the equation:    \(E=A\sigma T^4.\)
Both \(E,A\) are measured to an accuracy of \(1\%,\) while temperature \(T\) is measured to \(0.5\%.\) The error in the determination of \(\sigma\) is:
1. \(2\%\) 2. \(4\%\)
3. \(2.5\%\) 4. \(0.5\%\)
Subtopic:  Errors |
 71%
Level 2: 60%+

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The error in the measurement of distance is \(2\%,\) while that in time is \(1\%.\) The error in speed, computed from the above, is:
1. \(2\%+1\%\) 2. \(2\%-1\%\)
3. \(\dfrac{2\%+1\%}{2}\) 4. \(\dfrac{2\%-1\%}{2}\)
Subtopic:  Errors |
 83%
Level 1: 80%+

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The length of a rod, when measured once using a scale, has an absolute error of \(\Delta l \) – due to eye-estimation by the experimenter. This error may be considered to be small and random, with an equal probability to be positive as well as negative. If the experiment is repeated \(100\) times, and the average is taken, the error in the average will be:
1. \(\Delta l\) 2. \(\Large\frac{\Delta l}{10}\)
3. \(10\Delta l\) 4. \(100\Delta l\)
Subtopic:  Errors |
Level 3: 35%-60%

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