Units and Measurements Test - 16

1-Light year equal to \(9.4607\times10^{15}\) m and 9.4607 Pm

Pressure = \(\frac{Force}{Area} = ML^{-1}T^{-2}\)

Stress = \(\frac{Restroning\;force}{Area} = ML^{-1}T^{-2}\)

Angstrom (Å), unit of length used chiefly in measuring wavelengths of light, equal to \(10^{-10}\) metre, or 0.1 nanometres. It is named for the 19th-century Swedish physicist Anders Jonas Angstrom.

\(s = 3t^3 + 7t^2 + 4t + 8\)

\(\therefore v = \frac{ds}{dt}\)

\(v = 9t^2 + 14t + 4\)

\(\therefore a = \frac{dv}{dt} = \frac{d}{dt}(9t^2 + 14 t + 4)\)

a = 18t + 14

at t = 1 sec

a = 18 x 1 + 14

a = 32 \(m/s^2\)

It is the number of magnetic field lines passing through a surface (such as a loop of wire). The SI unit of magnetic flux is the Weber (Wb) (in derived units: volt-seconds).

Fathom is a unit of length equal to six feet. It is used to measure depth of sea.

The S.I. unit of Permittivity is Farad / meter.

Here, we know that.

1kw = 1000 watt

Or, 1hour = 3600 seconds

So, Putting these values,

1kwh = (1000w) x (3600s)

(w = \(\frac{j}{s}\))

1kwh = \(\frac{(3600000j)}{(s \times s)}\)

1kwh = 3.6 x 1000000 joule (mega = 1000000)

So, 1kwh = 3.6 mega joules

The largest practical unit of mass is Chandrasekhar limit.

1 C.S.L = 1.4 times mass of the Sun

Dry Ice is the common name for solid carbon dioxide (\(CO_2\)). It gets this name because it does not melt into a liquid when heated; instead, it changes directly into a gas (This process is known as sublimation).

Impulse = Force x time

= \([MLT^{-2}][T] = [MLT^{-1}]\)

Surface tension = \(\frac{Force}{length} = \frac{[MLT^{-2}]}{L}\) = \([ML^0T^{-2}]\)

Angular momentum = Moment of inertia x angular velocity

= \([ML^2][T^{-1}] = [ML^2T^{-1}]\)

Work Force x distance = \([MLT^{-2}][L] = [ML^2T^{-2}]\)

Energy = \([ML^2T^2]\)

Torque = Force x distance = \([MLT^2][L] = [ML^2 T^2]\)

Young's modulus

= \(\frac{\frac{Force}{Area}}{\frac{Change\;in\;length}{original\;length}}\)

= \(\frac{[MLT^{-2]}/[L^2]}{[L]/[L]}\) = \([ML^{-1}T^{-2}]\)

In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.
2.54 contain the least significant figures of 3

\(\frac{97.52}{2.54}=38.393=38.4\)

\(n = \frac{c}{v} = \frac{v \lambda_a}{v \lambda_g}\)

Hence \(\lambda_g = \frac{\lambda_a}{n}\)

= \(\frac{7200 Å}{1.5} = 4800 Å\)

The SI unit for heat capacity of an object is joule per Kelvin (J/K, or J \(K^{-1}\))

Unit of acceleration due to gravity is:

\(\mathrm{g=L^1T^{-2}}\)

If unit of both length and time is doubled then 

\(\mathrm{g'=(2L)^1(2T)^{-2}=\frac{1}{2}g}\)

Thus, the unit of acceleration due to gravity becomes halved. It means the numerical has to be doubled of original value so that we can get a constant value of g.

v = \(\frac{p}{2l}[\frac{F}{m}]^{1/2}\) ⇒ \(v^2 = \frac{P^2}{4l^2}[\frac{F}{m}]\)

\(\therefore m \propto \frac{F}{l^2v^2}\)

⇒ [m] = \(\Big[\frac{MLT^{-2}}{L^2T^{-2}} \Big]\) = \([ML^{-1}T^0]\)

\(\mathrm{X\,\alpha \,\frac{1}{N}}\)

\(\mathrm{\frac{X_1}{X_2} = \frac{N_2}{N_1}}\)

\(\mathrm{\Rightarrow\frac{X}{X'}= \frac{100}{10}}\)

\(\mathrm{\Rightarrow X'=\frac{10}{100}x}\)

\(\mathrm{\Rightarrow X'=\frac{x}{10}}\)

Density = \(\frac{Mass}{Volume}\)

= \(\frac{4.237}{2.5}\) = 1.6948 g/c.c

As per rules, the result of division will have two significant figures.

\(\therefore\) Density = 1.7g/c.c.

The light year and wavelength both have dimensions of distance and not of time. Therefore, assertion is true, both reasons is False.