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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 |
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An instrument with a small least count will have definitely:
| 1. | high accuracy and high precision |
| 2. | low accuracy and low precision |
| 3. | high accuracy |
| 4. | high precision |
Subtopic: Measurement & Measuring Devices |
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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. \(400\text{%}\)
1. \(100\text{%}\)
2. \(200\text{%}\)
3. \(300\text{%}\)
4. \(400\text{%}\)
Subtopic: Errors |
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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 |
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The speed of a distant star is observed to be \(1\) light-year/century. This value, when expressed in SI, is (approximately):
| 1. | \(3\times10^8~\text{m/s}\) | 2. | \(3\times10^6~\text{m/s}\) |
| 3. | \(3\times10^4~\text{m/s}\) | 4. | \(300~\text{m/s}\) |
Subtopic: Measurement & Measuring Devices |
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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 |
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Which of the following quantities have the same dimension?
1. B, C
2. A, B, C
3. B, D
4. A, B, C, D
| (A) | \(\dfrac{\text{(Magnetic flux)}^2}{\text{Electrical resistance}}\) | (B) | \(\text{Torque}\times\text{time}\) |
| (C) | \(\text{Momentum}\times\text{length}\) | (D) | \(\dfrac{\text{Power}}{\text{time}}\) |
2. A, B, C
3. B, D
4. A, B, C, D
Subtopic: Dimensions |
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Which of the quantities below have the same dimensions?
1. A, B
2. B, C
3. A, C
4. A, B, C
| (A) | \(\dfrac{\text{electric field }\times\text{ magnetic field}}{\mu_0}\) |
| (B) | \(\dfrac{\varepsilon_0\times\text{(electric potential)}^2\times\text{ velocity}}{\text{area}}\) |
| (C) | \(\dfrac{\text{power}}{\text{area}}\) |
2. B, C
3. A, C
4. A, B, C
Subtopic: Dimensions |
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The time taken by a pendulum to complete \(10\) oscillations is \(35.2\) seconds. What is the time period of a pendulum in seconds with appropriate significant figures?
1. \(3.52~\text s\)
2. \(3.5~\text s\)
3. \(3.520~\text s\)
4. \(3.6~\text s\)
1. \(3.52~\text s\)
2. \(3.5~\text s\)
3. \(3.520~\text s\)
4. \(3.6~\text s\)
Subtopic: Significant Figures |
From NCERT
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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. \(100\Delta l\)
1. \(\Delta l\)
2. \(\Large\frac{\Delta l}{10}\)
3. \(10\Delta l\)
4. \(100\Delta l\)
Subtopic: Errors |
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