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Q. No.The dimension of mutual inductance is:
1. [ML2 T–2 A –1]
2. [ML2T–3A –1]
3. [ML2T –2A –2]
4. [ML2T–3A–2]
Subtopic: Dimensions |
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A travelling microscope is used to determine the refractive index of a glass slab. If \(40\) divisions are there in \(1~\text{cm}\) on the main scale and \(50\) Vernier scale divisions are equal to \(49\) main scale divisions, then the least count of the travelling microscope is:
1. \(3\times 10^{-6}~\text{m}\)
2. \(4\times 10^{-6}~\text{m}\)
3. \(5\times 10^{-6}~\text{m}\)
4. \(6\times 10^{-6}~\text{m}\)
1. \(3\times 10^{-6}~\text{m}\)
2. \(4\times 10^{-6}~\text{m}\)
3. \(5\times 10^{-6}~\text{m}\)
4. \(6\times 10^{-6}~\text{m}\)
Subtopic: Measurement & Measuring Devices |
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Level 2: 60%+
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A silver wire has a mass \((0.6 \pm 0.006) \mathrm{g}\) radius \((0.5 \pm 0.005) \mathrm{mm}\) and length \((4 \pm 0.04) \mathrm{cm}\). The maximum percentage error in the measurement of its density will be:
1. 4%
2. 3%
3. 6%
4. 7%
1. 4%
2. 3%
3. 6%
4. 7%
Subtopic: Errors |
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The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be:
1. \(\mathrm{[ML^{–1}T^{–1}]}\)
2. \(\mathrm{[ML^{–1}T^{–2}]}\)
3. \(\mathrm{[ML^{2}T^{–1}]}\)
4. \(\mathrm{[M^{-1}L^{3}T^{0}]}\)
1. \(\mathrm{[ML^{–1}T^{–1}]}\)
2. \(\mathrm{[ML^{–1}T^{–2}]}\)
3. \(\mathrm{[ML^{2}T^{–1}]}\)
4. \(\mathrm{[M^{-1}L^{3}T^{0}]}\)
Subtopic: Dimensions |
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The distance of the Sun from Earth is \(1.5\times10^{11}\) m and its angular diameter is \((2000)\) s when observed from the earth. The diameter of the Sun will be:
1. \(2.45\times10^{10}\) m
2. \(1.45\times10^{10}\) m
3. \(1.45\times10^{9}\) m
4. \(0.14\times10^{9}\) m
1. \(2.45\times10^{10}\) m
2. \(1.45\times10^{10}\) m
3. \(1.45\times10^{9}\) m
4. \(0.14\times10^{9}\) m
Subtopic: Measurement & Measuring Devices |
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Level 3: 35%-60%
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If \(L,C~\text{and}~R\) are the self-inductance, capacitance, and resistance respectively, which of the following does not have the dimension of time?
1. \( RC \)
2. \(\dfrac{L}{R} \)
3. \(\sqrt{LC} \)
4. \( \dfrac{L}{C}\)
1. \( RC \)
2. \(\dfrac{L}{R} \)
3. \(\sqrt{LC} \)
4. \( \dfrac{L}{C}\)
Subtopic: Dimensions |
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Level 2: 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 |
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Velocity \((v)\) and acceleration \((a)\) in two systems of units \(1\) and \(2\) are related as \({v}_2=\dfrac{n}{m^2} {v}_1\) and \({a}_2=\dfrac{{a_1}}{mn} \) respectively. Here \(m\) and \(n\) are constants. The relations for distance and time in the two systems, respectively, are:
| 1. | \(\dfrac{n^3}{m^3}{L}_1={L}_2 ~\text{and}~ \dfrac{n^2}{m} {T}_1={T}_2 \) |
| 2. | \( L_1=\dfrac{n^4}{m^2} ~L_2~ \text{and} ~T_1=\dfrac{n^2}{m} T_2 \) |
| 3. | \( L_1=\dfrac{n^2}{m} L_2~\text{and}~T_1=\dfrac{n^4}{m^2} T_2 \) |
| 4. | \( \dfrac{n^2}{m}{L}_1={L}_2~ \text{and}~\dfrac{n^4}{m^2} {T}_1={T}_2\) |
Subtopic: Dimensions |
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A student in the laboratory measured thickness of a wire using a screw gauge. The readings are \(1.22\) mm, \(1.23\) mm, \(1.19\) mm and \(1.20\) mm. The percentage error is \(\dfrac{x}{121}\%\). The value of \(x\) is:
1. \(100\)
2. \(200\)
3. \(150\)
4. \(300\)
1. \(100\)
2. \(200\)
3. \(150\)
4. \(300\)
Subtopic: Errors |
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Level 2: 60%+
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An expression for a dimensionless quantity P is given by \(P=\frac{\alpha}{\beta} \log _e\left(\frac{\mathrm{kt}}{\beta \mathrm{x}}\right)\); where \(\alpha \) and \(\beta\) are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimension of \(\alpha \) will be :
1. \(\left[\mathrm{M}^0 \mathrm{~L}^{-1} \mathrm{~T}^0\right] \)
2. \(\left[\mathrm{ML}^0 \mathrm{~T}^{-2}\right] \)
3. \(\left[\mathrm{MLT}^{-2}\right] \)
4. \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]\)
1. \(\left[\mathrm{M}^0 \mathrm{~L}^{-1} \mathrm{~T}^0\right] \)
2. \(\left[\mathrm{ML}^0 \mathrm{~T}^{-2}\right] \)
3. \(\left[\mathrm{MLT}^{-2}\right] \)
4. \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]\)
Subtopic: Dimensions |
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Level 2: 60%+
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