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A metal wire has mass $$(0.4\pm 0.002)~\mathrm{g}$$, radius $$(0.3\pm 0.001)~\mathrm{mm}$$ and length $$(5\pm 0.02)~\mathrm{cm}$$. The maximum possible percentage error in the measurement of density will nearly be: 1. $$1.4 \%$$ 2. $$1.2 \%$$ 3. $$1.3 \%$$ 4. $$1.6 \%$$

Subtopic:  Errors |
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The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are:
1. Random errors
2. Instrumental errors
3. Personal errors
4. Least count errors
Subtopic:  Errors |
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The diameter of a spherical bob, when measured with vernier callipers yielded the values: $$3.33$$ cm, $$3.32$$ cm, $$3.34$$ cm, $$3.33$$ cm and $$3.32$$ cm. The mean diameter to appropriate significant figures is:
1. $$3.328$$ cm
2. $$3.3$$ cm
3. $$3.33$$ cm
4. $$3.32$$ cm
Subtopic:  Measurement & Measuring Devices |
55%
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The mechanical quantity, which has dimensions of reciprocal of mass $$(M^{-1}),$$ is:
 1 angular momentum 2 coefficient of thermal conductivity 3 torque 4 gravitational constant
Subtopic:  Dimensions |
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The percentage error in the measurement of $$g$$ is:
[Given,  $$g=\frac{4\pi^2L}{T^2},L=(10\pm0.1)~\text{cm, }T=(100\pm1)~\text s$$]
1. $$2\%$$
2. $$5\%$$
3. $$3\%$$
4. $$7\%$$
Subtopic:  Errors |
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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
Subtopic:  Dimensions |
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The determination of the value of acceleration due to gravity $$(g)$$ by simple pendulum method employs the formula,
$$g=4\pi^2\frac{L}{T^2}$$
The expression for the relative error in the value of $$g$$ is:

 1 $$\frac{\Delta g}{g}=\frac{\Delta L}{L}+2\Big(\frac{\Delta T}{T}\Big)$$ 2 $$\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}-2\frac{\Delta T}{T}\Big]$$ 3 $$\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}+2\frac{\Delta T}{T}\Big]$$ 4 $$\frac{\Delta g}{g}=\frac{\Delta L}{L}-2\Big(\frac{\Delta T}{T}\Big)$$
Subtopic:  Errors |
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When the circular scale of a screw gauge completes $$2$$ rotations, it covers $$1$$ mm over the pitch scale. The total number of circular scale divisions is $$50$$. The least count of the screw gauge in metres is:
1. $$10^{-4}$$
2. $$10^{-5}$$
3. $$10^{-2}$$
4. $$10^{-3}$$

Subtopic:  Measurement & Measuring Devices |
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Match List-I with List-II.

 List-I List-II (a) Gravitational constant ($$G$$) (i) $$[{L}^2 {~T}^{-2}]$$ (b) Gravitational potential energy (ii) $$[{M}^{-1} {~L}^3 {~T}^{-2}]$$ (c) Gravitational potential (iii) $$[{LT}^{-2}]$$ (d) Gravitational intensity (iv) $$[{ML}^2 {~T}^{-2}]$$

Choose the correct answer from the options given below:
 (a) (b) (c) (d) 1. (iv) (ii) (i) (iii) 2. (ii) (i) (iv) (iii) 3. (ii) (iv) (i) (iii) 4. (ii) (iv) (iii) (i)
Subtopic:  Dimensions |
70%
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The area of a rectangular field (in $$\mathrm{m^2}$$) of length $$55.3$$ m and breadth $$25$$ m after rounding off the value, for correct significant digits is:
1. $$14\times10^{2}$$
2. $$138\times10^{1}$$
3. $$1382$$
4. $$1382.5$$
Subtopic:  Significant Figures |
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