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Q. No.The determination of the value of acceleration due to gravity \((g)\) by simple pendulum method employs the formula,
\(g=4\pi^2\dfrac{L}{T^2}\)
The expression for the relative error in the value of \(g\) is:
1.
\(\dfrac{\Delta g}{g}=\dfrac{\Delta L}{L}+2\Big(\dfrac{\Delta T}{T}\Big)\)
2.
\(\dfrac{\Delta g}{g}=4\pi^2\Big[\dfrac{\Delta L}{L}-2\dfrac{\Delta T}{T}\Big]\)
3.
\(\dfrac{\Delta g}{g}=4\pi^2\Big[\dfrac{\Delta L}{L}+2\dfrac{\Delta T}{T}\Big]\)
4.
\(\dfrac{\Delta g}{g}=\dfrac{\Delta L}{L}-2\Big(\dfrac{\Delta T}{T}\Big)\)
\(g=4\pi^2\dfrac{L}{T^2}\)
The expression for the relative error in the value of \(g\) is:
Subtopic: Errors |
78%
Level 2: 60%+
NEET - 2022
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A specially designed Vernier calliper has the main scale least count of \(1~\text{mm}.\) On the Vernier scale, there are \(10\) equal divisions and they match with \(11\) main scale divisions. Then, the least count of the Vernier calliper is:
1. \(0.1~\text{mm}\)
2. \(0.909~\text{mm}\)
3. \(1.1~\text{mm}\)
4. \(0.09~\text{mm}\)
1. \(0.1~\text{mm}\)
2. \(0.909~\text{mm}\)
3. \(1.1~\text{mm}\)
4. \(0.09~\text{mm}\)
Subtopic: Measurement & Measuring Devices |
69%
Level 2: 60%+
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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 |
53%
Level 3: 35%-60%
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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 |
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Level 3: 35%-60%
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In Vander Wall's equation \(\left[{P}+\dfrac{{a}}{{V}^{2}}\right][{V}-{b}]={RT}\); \(P\) is pressure, \(V\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The ratio of constants \(\dfrac a b\) is dimensionally equal to:
| 1. | \(\dfrac P V\) | 2. | \(\dfrac V P\) |
| 3. | \(PV\) | 4. | \(PV^3\) |
Subtopic: Dimensions |
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Level 2: 60%+
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The angle of \(1'\) (minute of arc) is nearly equal to:
(use \(2\pi=360^\circ \) and \(\pi=3.14 \))
(use \(2\pi=360^\circ \) and \(\pi=3.14 \))
| 1. | \(2.42\times10^{-6} \) rad | 2. | \(2.85\times10^{-6} \) rad |
| 3. | \(2.91\times10^{-4} \) rad | 4. | \(1.75\times10^{-2} \) rad |
Subtopic: Measurement & Measuring Devices |
65%
Level 2: 60%+
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Match List-I with List-II.
Choose the correct answer from the options given below:
| List-I | List-II | ||
| \(\mathrm{(A)}\) | Torque | \(\mathrm{(I)}\) | N-m s-1 |
| \(\mathrm{(B)}\) | Stress | \(\mathrm{(II)}\) | J-kg-1 |
| \(\mathrm{(C)}\) | Latent Heat | \(\mathrm{(III)}\) | N-m |
| \(\mathrm{(D)}\) | Power | \(\mathrm{(IV)}\) | N-m-2 |
Choose the correct answer from the options given below:
| 1. | \(\mathrm{A-III, B-II, C-I, D-IV}\) |
| 2. | \(\mathrm{A-III, B-IV, C-II, D-I}\) |
| 3. | \(\mathrm{A-IV, B-I, C-III, D-II}\) |
| 4. | \(\mathrm{A-II, B-III, C-I, D-IV}\) |
Subtopic: Dimensions |
85%
Level 1: 80%+
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The number of significant figures in the physical quantity \(2.56\times 10^5\) kg is/are:
| 1. | \(1\) | 2. | \(2\) |
| 3. | \(3\) | 4. | \(5\) |
Subtopic: Significant Figures |
91%
Level 1: 80%+
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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 |
77%
Level 2: 60%+
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The physical quantity that has the same dimensional formula as pressure is:
1. Force
2. Momentum
3. Young's modulus of elasticity
4. Coefficient of viscosity
1. Force
2. Momentum
3. Young's modulus of elasticity
4. Coefficient of viscosity
Subtopic: Dimensions |
81%
Level 1: 80%+
NEET - 2022
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