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Q. No.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 4: Below 35%
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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 |
Level 3: 35%-60%
Hints
What is the unit of the quantity represented by: \(\dfrac{\text{(Angular momentum)}}{\text{(electric charge)}^2}\)
1. \(\Omega\) (ohm)
2. s/m
3. \(\text{H }\)(henry)
4. \(\text{F }\) (farad)
1. \(\Omega\) (ohm)
2. s/m
3. \(\text{H }\)(henry)
4. \(\text{F }\) (farad)
Subtopic: Dimensions |
56%
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%
Hints
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 |
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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