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# The angle of $$1'$$ (minute of an arc) in radian is nearly equal to: 1. $$2.91 \times 10^{-4} ~\mathrm{rad}$$ 2. $$4.85 \times 10^{-4} ~\mathrm{rad}$$ 3. $$4.80 \times 10^{-6} ~\mathrm{rad}$$ 4. $$1.75 \times 10^{-2} ~\mathrm{rad}$$

Subtopic: Â Measurement & Measuring Devices |
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The angle of $$1^\circ$$ (degree) will be equal to:
(Use $$360^\circ=2\pi$$ rad
)
1. $$1.034\times10^{-3}$$ rad
2. $$1.745\times10^{-2}$$ rad
3. $$1.524\times10^{-2}$$ rad
4. $$1.745\times10^{3}$$ rad

Subtopic: Â Measurement & Measuring Devices |
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Each side of a cube is measured to be $$7.203$$ $$\mathrm{m}.$$ What are the total surface area and the volume respectively of the cube to appropriate significant figures?

 1 $$373.7~\mathrm{m^2}$$ and $$311.3~\mathrm{m^3}$$ 2 $$311.3~\mathrm{m^2}$$ and $$373.7~\mathrm{m^3}$$ 3 $$311.2992~\mathrm{m^2}$$ and $$373.7147~\mathrm{m^3}$$ 4 $$373.7147~\mathrm{m^2}$$ and $$311.2992~\mathrm{m^3}$$

Subtopic: Â Significant Figures |
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On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is/are not correct.
a. $$y = a\sin \left(2\pi t / T\right)$$
b. $$y = a\sin(vt)$$
c. $$y = \left({a \over T}\right) \sin \left({t \over a}\right)$$
d. $$y = a \sqrt 2 \left(\sin \left({2 \pi t \over T}\right) - \cos \left({2 \pi t \over T}\right)\right)$$
(Symbols have their usual meanings.)
Choose the correct option:
1. (a), (c)
2. (a), (b)
3. (b), (c)
4. (a), (d)

Subtopic: Â Dimensions |
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If momentum ($$\mathrm{p}$$), area ($$\mathrm{A}$$), and time ($$\mathrm{T}$$) are taken to be fundamental quantities, then energy has the dimensional formula:
1. $${\left[\mathrm{pA}^{-1} \mathrm{~T}^1\right]}$$
2. $${\left[\mathrm{p}^2 \mathrm{AT}\right]}$$
3. $${\left[\mathrm{pA}^{-1 / 2} \mathrm{~T}\right]}$$
4. $${\left[\mathrm{pA}^{1 / 2} \mathrm{~T}^{-1}\right]}$$

Subtopic: Â Dimensions |
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Young's modulus of steel is $$1.9 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$$. When expressed in CGS units of $$\mathrm{dyne/cm^2}$$, it will be equal to: $$(1 \mathrm{~N}=10^5 \text { dyne, } 1 \mathrm{~m}^2=10^4 \mathrm{~cm}^2)$$
1. $$1.9 \times 10^{10}$$
2. $$1.9 \times 10^{11}$$
3. $$1.9 \times 10^{12}$$
4. $$1.9 \times 10^9$$

Subtopic: Â Dimensions |
Â 73%
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The numbers $$2.745$$ and $$2.735$$ on rounding off to $$3$$ significant figures will give respectively,

 1 $$2.75$$  and $$2.74$$ 2 $$2.74$$  and $$2.73$$ 3 $$2.75$$ and $$2.73$$ 4 $$2.74$$ and $$2.74$$
Subtopic: Â Significant Figures |
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The mass and volume of a body are $$4.237~\mathrm{g}$$ and $$2.5~\mathrm{cm^3}$$, respectively. The density of the material of the body in correct significant figures will be:
1. $$1.6048~\mathrm{g~cm^{-3}}$$
2. $$1.69~\mathrm{g~cm^{-3}}$$
3. $$1.7~\mathrm{g~cm^{-3}}$$
4. $$1.695~\mathrm{g~cm^{-3}}$$

Subtopic: Â Significant Figures |
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The sum of the numbers $$436.32,227.2,$$ and $$0.301$$ in the appropriate significant figures is:

 1 $$663.821$$ 2 $$664$$ 3 $$663.8$$ 4 $$663.82$$
Subtopic: Â Significant Figures |
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A physical quantity is measured and the result is expressed as $$nu$$ where $$u$$ is the unit used and $$n$$ is the numerical value. If the result is expressed in various units then:
1. $$n\propto \mathrm{size~of}~u$$
2. $$n\propto u^2$$
3. $$n\propto \sqrt u$$
4. $$n\propto \frac{1}{u}$$

Subtopic: Â Dimensions |
Â 76%
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