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Q. No.Students \(A, B\) and \(C\) measure the length of a room using a \(25~\text{m}\) long measuring tape of least count \((\mathrm{LC})~0.5~\text{cm}\), a meter-scale of \((\mathrm{LC})~0.1~\text{cm}\) and a foot-scale of \((\mathrm{LC})~0.05~\text{cm}\), respectively. If the specified length of the room is \(9.5~\text{m},\) then which of the following students will report the lowest relative error in the measured length?
1. Student \(A\)
2. Student \(B\)
3. Student \(C\)
4. Both students \(B\) and \(C\)
1. Student \(A\)
2. Student \(B\)
3. Student \(C\)
4. Both students \(B\) and \(C\)
Subtopic: Errors |
Level 4: Below 35%
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If the error in the measurement of the momentum of a particle is \((+100\text{%}) \) then the error in the measurement of kinetic energy is:
| 1. | \(100\text{%}\) | 2. | \(200\text{%}\) |
| 3. | \(300\text{%}\) | 4. | \(400\text{%}\) |
Subtopic: Errors |
Level 4: Below 35%
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In an experiment to find the acceleration due to gravity \((g)\) using a simple pendulum, the time period of \(0.5\) s is measured from the time of \(100\) oscillations with a watch of \(1\) s resolution. If the measured value of length is \(10\) cm known to \(1\) mm accuracy. The accuracy in the determination of \(g\) is found to be \(x\text{%}.\) The value of \(x \) is:
1. \(2\)
2. \(4\)
3. \(5\)
4. \(7\)
1. \(2\)
2. \(4\)
3. \(5\)
4. \(7\)
Subtopic: Errors |
Level 3: 35%-60%
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A rigid spherical body is spinning around an axis without any external torque. Due to temperature, its volume increases by \(3\%\). The percentage change in its angular speed is:
| 1. | \(-2\%\) | 2. | \(-1\%\) |
| 3. | \(-3\%\) | 4. | \(1\%\) |
Subtopic: Errors |
Level 3: 35%-60%
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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%
Hints
A student measures the time period of \(100\) oscillations of a simple pendulum four times. That data set is \(90\) s, \(91\) s, \(95\) s and \(92\) s. If the minimum division in the measuring clock is \(1\) s, then the reported mean time should be:
1. \(92\pm 5.0\ \)s
2. \(92\pm 1.8\ \)s
3. \(92\pm 3\ \)s
4. \(92\pm 2\ \)s
1. \(92\pm 5.0\ \)s
2. \(92\pm 1.8\ \)s
3. \(92\pm 3\ \)s
4. \(92\pm 2\ \)s
Subtopic: Errors |
Level 3: 35%-60%
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Two measured quantities are given by \(A=(1.0~\text{m} \pm0.2 ~\text{m})\) and \(B=(2.0~\text{m} \pm0.2 ~\text{m}).\) What is the reported value of \(\sqrt{AB}~?\)
1. \((1.4 ~\text{m}\pm0.4~ \text{m})\)
2. \((1.4 1~\text{m}\pm0.4~ \text{m})\)
3. \((1.4 ~\text{m}\pm0.2~ \text{m})\)
4. \((2 ~\text{m}\pm0.2~ \text{m})\)
1. \((1.4 ~\text{m}\pm0.4~ \text{m})\)
2. \((1.4 1~\text{m}\pm0.4~ \text{m})\)
3. \((1.4 ~\text{m}\pm0.2~ \text{m})\)
4. \((2 ~\text{m}\pm0.2~ \text{m})\)
Subtopic: Errors |
55%
Level 3: 35%-60%
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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
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%
Hints
- 1(current)
Q. No.
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