Physical Quantities and Measurement Test - 6

Speed is defined as the ratio of distance covered to the time taken. The speed of a moving body is the distance travelled by it in unit time. If the distance is in km and time is in hours, then the speed is km/hr. If the distance is in m and the time is in seconds, then the speed is m/sec.

Speed   v = $\frac{\mathrm{Distance}}{\mathrm{Time}}$

Length and time are the fundamental quantities involved here to compare the speed of Ram and Shyam.

The pascal (Pa)(Pa) is the SI derived unit of pressure used to quantify internal pressure, stress, Young's modulus and ultimate tensile strength. The unit, named after Blaise Pascal, is defined as one newton per square metre.

Since z = ax + bx², unit of bx² must be that of zz.

Hence the unit of b is that of $\frac{z}{x^2}$

which is km/h²

Light travels at approximately 300,000 kilometers per second in a vacuum, which has a refractive index of 1.0, but it slows down to 225,000 kilometers per second in water (refractive index = 1.3) and 200,000 kilometers per second in glass (refractive index of 1.5). The interaction of the light with the particles in the medius causes the delay.

Unit of g in SI is ms⁻¹ and that of G is Nm ² kg⁻²

Where 1 N = 1 kg ms⁻²  (in MKS system)

So, MKS units of G is m³s⁻²kg⁻¹

Thus CGS unit of g is cm s⁻² and that of G is cm³s⁻²g⁻¹

Thus CGS unit of g/G is g cm⁻²

The gram per cubic centimetre is a unit of density in the CGS system, defined as mass in grams divided by volume in cubic centimetres. The SI unit of kilogram per cubic metre (kg/m3) and the cgs unit of gram per cubic centimetre (g/cm3) are probably the most commonly used units fordensity. 1,000 kg/m3 equals 1 g/cm3. (The cubic centimeter can be alternately called a millilitre or a cc.)

The International System of Units, universally abbreviated S.I. is the modern metric system of measurement. The S.I. was established in 1960 by the 11th General Conference on Weights and Measures.

\(e=\frac{d \phi}{d t}=L \frac{d I}{d t}\)

\(\Rightarrow[\text {volt}]=\frac{[\text {weber}]}{[\text {second}]}=[L] \frac{[\text {Ampere}]}{[\text {second}]}\)

also,

Energy dissipated(E) \(=V I t\)

\(\Rightarrow[\text {Joule}]=[\text {volt}][\text {Ampere}][\text {second}]\) Rightarrow\([\text {volt}-\text {second}]=\frac{[\text {Joule}]}{[\text {Ampere}]}\)

so units of self inductance L is,

\([L]=\frac{w e b e r}{\text { Ampere }}=\frac{\text { volt }-\text { second }}{\text { Ampere }}=\frac{\text { Joule }}{\text { Ampere }^{2}}\)

S.I system (standard international system).

In this system the units of mass, length and time are same, as that of M.K.S system.

However, it is an enlarged system encompassing all fundamental units.

Electron volt or \(e V\) is the unit of energy (electrical energy). \(1 e V=1.6 \times 10^{-19}\) coulombs (charge of an electron) \(\times 1\) volt.

Temperature is measured in Kelvin which is represented by K

Thus, 10 K is the correct representation of temperature.

Ampere-hour is the unit of quantity of electricity or quantity of electric charge.

Power is measured in Watt.

Energy is measured in Joules.

Strength of current ia measured in Amperes.

Impulse is defined as the change in momentum and thus impulse has the unit of momentum i.e.  kg m/s. The newton-second (also newton second; symbol: N⋅s or N s) is the derived SI unit of impulse. It is dimensionally equivalent to the momentum unit kilogram-metre per second (kg⋅m/s). One newton-second corresponds to a one-newton force applied for one second.

The kilowatt hour is a unit of energy equal to 1,000 watt-hours, or 3.6 megajoules. If the energy is being transmitted or used at a constant rate (power) over a period of time, the total energy in kilowatt-hours is the product of the power in kilowatts and the time in hours. The kilowatt-hour is commonly used as a billing unit for energy delivered to consumers by electric utilities.

From BiotSavart's law
$B=\frac{{\mu }_0}{4\mathrm{\pi }}\frac{i.dl\sin \theta }{r^2}$

${\mu }_0=\frac{4{\mathrm{\pi Br}}^2}{idl\sin \theta }=\frac{Wb{m}^{-2}{m}^2}{A.m}=Wb{A}^{-1}{m}^{-1}$