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Q. No.Which of the quantities below have the same dimensions?
(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)
\(\dfrac{\text{power}}{\text{area}}\)
1. A, B
2. B, C
3. A, C
4. A, B, C
Subtopic: Dimensions |
Level 3: 35%-60%
Hints
Darcy's law describes the volume flow rate \((Q) \) of a viscous fluid (viscosity : \(\mu\)) through a porous medium, under the action of a pressure difference. \(\dfrac{Q}{A}=\dfrac{k}{\mu}\left(\dfrac{{\large p}_{1}-{\large p}_{2}}{L}\right) \)
Here, \(k\) is the permeability of the medium. The unit of \(k\) is (SI units):
Here, \(k\) is the permeability of the medium. The unit of \(k\) is (SI units):
| 1. | m | 2. | m2 |
| 3. | m2/s | 4. | m/s2 |
Subtopic: Dimensions |
52%
Level 3: 35%-60%
Hints
Which, of the following, is dimensionless?
| 1. | \(\text{impedance}\times\text{conductance} \) | 2. | \(\dfrac{\text{emissive power}}{\text{emissivity}}\) |
| 3. | \(\dfrac{\text{electric field}}{\text{magnetic field}}\) | 4. | \(\dfrac{\text{inductance}}{\text{capacitance}}\) |
Subtopic: Dimensions |
Level 3: 35%-60%
Hints
A screw gauge of pitch \(0.5\) mm is used to measure the diameter of uniform wire of length \(6.8\) cm, the main scale reading is \(1.5\) mm and circular scale reading is \(7\). The calculated curved surface area of wire to the appropriate significant figures is:
[Screw gauge has \(50\) divisions on the circular scale]
1. \(6.8\) cm2
2. \(3.4\) cm2
3. \(3.9\) cm2
4. \(2.4\) cm2
[Screw gauge has \(50\) divisions on the circular scale]
1. \(6.8\) cm2
2. \(3.4\) cm2
3. \(3.9\) cm2
4. \(2.4\) cm2
Subtopic: Measurement & Measuring Devices |
52%
Level 3: 35%-60%
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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%
Hints
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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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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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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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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The quantity \(\eta\) is defined by: \(\eta=\dfrac{1}{\mu_0\sigma}\)
where \(\mu_0\) is the permeability of free space and \(\sigma\) is the electrical conductivity (of a plasma). \(\eta\) is referred to as the magnetic diffusivity. Its SI unit is:
1. m2/s
2. m/s2
3. C-m2/s
4. T-m/s
where \(\mu_0\) is the permeability of free space and \(\sigma\) is the electrical conductivity (of a plasma). \(\eta\) is referred to as the magnetic diffusivity. Its SI unit is:
1. m2/s
2. m/s2
3. C-m2/s
4. T-m/s
Subtopic: Dimensions |
Level 3: 35%-60%
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