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Q. No.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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The quantity: \({\mathcal P}=\int|\psi(\vec r)|^2dV,\) is the probability of finding a particle in the given volume. The integration is carried over the given volume. The dimension of \(|\psi(\vec r)|\) is:
1. \(L^{-3}\)
2. \(L^{-3/2}\)
3. \(L^{3/2}\)
4. \(M^0L^0T^0\)
1. \(L^{-3}\)
2. \(L^{-3/2}\)
3. \(L^{3/2}\)
4. \(M^0L^0T^0\)
Subtopic: Dimensions |
Level 3: 35%-60%
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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. \(300~\text{m/s}\)
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 |
Level 3: 35%-60%
Hints
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 |
56%
Level 3: 35%-60%
Hints
The quantities \(K,c,\eta \) represent the thermal conductivity, the specific heat capacity and the viscosity of a liquid. Which of the following, is dimensionless?
| 1. | \(Kc\eta\) | 2. | \(\dfrac{Kc}{\eta}\) |
| 3. | \(\dfrac{K\eta}{c}\) | 4. | \(\dfrac{\eta c}{K}\) |
Subtopic: Dimensions |
53%
Level 3: 35%-60%
Hints
Given below are two statements:
| Assertion (A): | The product of pressure \((\mathrm{P})\) and time \((\mathrm{t})\) has the same dimension as that of the coefficient of viscosity. |
| Reason (R): | \(\text { Coefficient of viscosity }=\frac{\text { Force }}{\text { Velocity gradient }}\) |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Dimensions |
53%
Level 3: 35%-60%
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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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Hints
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Consider the efficiency of Carnot’s engine is given by \(\eta=\dfrac{\alpha \beta}{\sin \theta} \log _{{e}} \dfrac{\beta {x}}{{kT}}\), where \(\alpha\) and \(\beta\) are constants. If \(T\) is temperature, \(k\) is Boltzman constant, \(\theta\) is angular displacement and \(x\) has the dimensions of length.
Which of the following statements is incorrect?
Which of the following statements is incorrect?
| 1. | The dimensions of \(\beta\) are same as that of force. |
| 2. | The dimensions of \(\alpha^{-1}x\) are same as that of energy. |
| 3. | The dimensions of \(\eta^{-1} \sin \theta\) are same as that of \(\alpha \beta\). |
| 4. | The dimensions of \(\alpha\) same as that of \(\beta\). |
Subtopic: Dimensions |
53%
Level 3: 35%-60%
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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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In a Vernier Calipers. \(10\) divisions of the Vernier scale is equal to the \(9\) divisions of the main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and \(4\)th Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to \(1\) mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between \(30\) and \(31\) divisions of main scale reading and \(6\)th Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be:
1. \(3.02~\text{cm}\)
2. \(3.06~\text{cm}\)
3. \(3.10~\text{cm}\)
4. \(3.20~\text{cm}\)
1. \(3.02~\text{cm}\)
2. \(3.06~\text{cm}\)
3. \(3.10~\text{cm}\)
4. \(3.20~\text{cm}\)
Subtopic: Measurement & Measuring Devices |
53%
Level 3: 35%-60%
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