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# The radius of a circle is stated as $$2.12$$ cm. Its area should be written as: 1. $$14\mathrm{~cm^2}$$ 2. $$14.1\mathrm{~cm^2}$$ 3. $$14.11\mathrm{~cm^2}$$ 4. $$14.1124\mathrm{~cm^2}$$

Subtopic: Â Significant Figures |
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The dimensions of $$\left [ML^{-1} T^{-2} \right ]$$ may correspond to:

 a. work done by a force b. linear momentum c. pressure d. energy per unit volume

Choose the correct option:

 1 (a) and (b) 2 (b) and (c) 3 (c) and (d) 4 none of the above

Subtopic: Â Dimensions |
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$$\int \frac{\mathrm{dx}}{\sqrt{2 \mathrm{ax}-\mathrm{x}^{2}}}=\mathrm{a}^{\mathrm{n}} \sin ^{-1}\left[\frac{\mathrm{x}}{\mathrm{a}}-1\right]$$
The value of $$\mathrm{n}$$ is:
1. $$0$$
2. $$-1$$
3. $$1$$
4. none of these

Subtopic: Â Dimensions |
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A dimensionless quantity,

 1 never has a unit 2 always has a unit 3 may have a unit 4 does not exist
Subtopic: Â Dimensions |
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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 |
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Which of the following equations is dimensionally correct?
$$(I)~~ v=\sqrt{\frac{P}{\rho}}~~~~~~(II)~~v=\sqrt{\frac{mgl}{I}}~~~~~~(III)~~v=\frac{Pr^2}{2\eta l}$$
(where  $$v=$$ speed, $$P=$$ pressure; $$r,$$ $$l$$ are lengths; $$\rho=$$  density, $$m=$$ mass, $$g=$$ acceleration due to gravity, $$I=$$ moment of inertia, and $$\eta=$$ coefficient of viscosity)

 1 $$I~ and~II$$ 2 $$I~ and~III$$ 3 $$II~ and~III$$ 4 $$I,~II~and~III$$
Subtopic: Â Dimensions |
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The acceleration due to gravity on the surface of the earth is $$g=10$$ m/s2. The value in km/(minute)2 is:
1. $$36$$
2. $$0.6$$
3. $$\frac{10}{6}$$
4. $$3.6$$

Subtopic: Â Dimensions |
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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.    $$\frac{Q}{A}=\frac{k}{\mu}\left(\frac{{\large p}_{1}-{\large p}_{2}}{L}\right)$$
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: Â Dimensions |
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Plane angle and solid angle have:
 1 both units and dimensions 2 units but no dimensions 3 dimensions but no units 4 no units and no dimensions
Subtopic: Â Dimensions |
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The area of a rectangular field (in $$\text{m}^2$$) 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: Â Significant Figures |
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