Physical Quantities and Measurement Test - 8

$\frac{dyne}{c{m}^2}=\frac{\left[M^1{L}^1{T}^{-2}\right]}{L^2}=\left[M^1{L}^{-1}{T}^{-2}\right]$

Pressure =forceArea=$\frac{Force}{Area}$=$\frac{M^1{L}^1{T}^{-2}}{L^2}$ $\left[M^1{L}^{-1}{T}^{-2}\right]$

Longitudinal stress = Young's Modulus $= \left[M^1{L}^{-1}{T}^{-2}\right]$

Longitudinal strain = $\frac{∆l}{l}$ $=\left[M^{ 0}{L}^0{T}^0\right]$

Hence, option C is correct.

Quantity       Dimension

Energy \(\quad \mathrm{M} L^{2} \mathrm{T}^{-2}\)

Work \(\quad \mathrm{M} L^{2} \mathrm{T}^{-2}\)

Power \(\quad \mathrm{M} L^{2} \mathrm{T}^{-3}\)

So, the dimension of energy and work is same but different to power.

Option (C) is correct.

1 milligram (mg) = 10⁻³ gram (g)

Hence option B is correct

Density of object is defined as the mass of the body per unit is volume.

Density = $\frac{mass}{volume}$

Thus option A is correct.

Susceptibility is unit less.

Magnetic flux is expressed Vs or [M¹L²T⁻²A⁻¹] = JA⁻¹ .

Hence, option B is correct.

SI unit system contains seven fundamental quantities which are independent to each other and can be used to represent any given quantity. Hence, all physical quantities can be represented in powers of seven fundamental SI units.

Hence option D is correct

The debye (symbol: D) is a CGS unit of electric dipole moment, named in the honour of the physicist Peter J. W. Debye.

It is defined as 1×10⁻¹⁸statcoulomb - centimetre.

Hence option D is correct

1 micron \(=10^{-6} \mathrm{m}\)

1 nano meter \(=10^{-9} \mathrm{m}\)

1 micron \(=10^{-6} \mathrm{mt}=10^{-6} \frac{\text { nano }}{10^{-9}}\)

1 micron \(=10^{3}\) nanometer

Stress has the units of Force/Area = N/m², while strain (=Δl/l) is dimensionless. So option A is correct.

Surface tension is Force/Length, thus N/m, hence B is also correct.

Energy has the units of [ML²T⁻²], hence the units have to be kgm²/s². Thus C is incorrect option.

Pressure is Force/Area = N/m², thus D is again correct.

Acceleration has unit m/s².

The rate of change of acceleration $\frac{\overrightarrow{da}}{dt}=\frac{d^{2}y}{d{t}^2}=\frac{m}{s^3}$

Hence, option B is correct.

The ratio of increase in resistance per degree rise in temperature to its resistance at 0⁰C is defined as the temperature coefficient of resistance (α).
$A=\frac{Rt-R_0}{R_{0}t},$

The unit of α is K⁻¹.

Thus option B is correct.

The unity of density= $\frac{unit of mass}{{\left(unit of lenth\right)}^B}$
= (pails)(jack)^-3

Hence option B is correct

Joule is a unit of energy and second is the unit of time.

Thus, Joule × second has dimensions ML²T⁻² × T = ML²T⁻¹

Now, energy cannot be the answer since energy has Joule as its unit and cannot be Joule-seconds.

Momentum can't be the answer as momentum is force X time which has dimensions MLT⁻¹

Angular momentum is given by cross product of linear momentum and radius vector thus it has dimensions MLT⁻¹× L = ML²T⁻¹, which is the correct answer.

Finally, Power is force times velocity, so its dimensions are MLT⁻² × LT⁻¹ = ML²T^-3

Hence option C is correct

Electromotive force is the voltage developed by any source of electrical energy such as a battery or dynamo. It is generally defined as the electrical potential for a source in a circuit.

It is not a force but voltage and its unit is volt.

Electric intensity at a point is defined as the force experienced per unit positive charge at a point placed in the electric field.

Its unit is Newton/Coloumb=NC⁻¹

Both statements are wrong.

Thus option B is correct.

The significant figures are the number of digits in a value that are significant. In 2.08m, the number of significant figures is 3. In the answer also we must maintain 3 significant figures only. Hence option B is correct