Units and Measurements Test - 15

Light year is a distance which light travels in one year.

Unit of energy will be

\(\frac{kg-m^2}{sec^2}\)

1 nm = \(10^{-9}\) m 

= \(10^{-7}\) cm

\(ct^2\) must have dimensions of L ⇒ c must have dimensions of \(\frac{L}{T^2}\) i.e. \(LT^{-2}\).

\(E = -\frac{dV}{dx}\)

Energy (E) = F x d

F = \(\frac{E}{d}\)

So \(\frac{Erg}{metre}\) can be the unit of force.

SI unit of permeability is Henry per metre, Tesla metre per ampere, Weber per ampere metre.

1 kWh = 1 x \(10^3\) x 3600 W x sec

= 36 x \(10^5 J\)

1fermi = \(10^{-15} \) metre

Liquids and gases which have ability to flow are called Fluids.

Reynolds number and coefficient of friction are dimensionless.

6 × \(10^{-5}\) = 60 × \(10^{-6}\) = 60 microns

Mach number = \(\frac{Velocity \;of\;object}{Velocity\;of\;sound}\)

\(n_2 = n_1\Big[\frac{L_1}{L_2} \Big ]^1\Big[\frac{T_1}{T_2} \Big ]^{-2}\)

= 10 \(\Big[\frac{meter}{km} \Big ]^1 \Big[\frac{sec}{hr} \Big ]^{-2}\)

\(n_2 = 10 \Big [\frac{m}{10^3 m} \Big ] \Big[\frac{sec}{3600\; sec} \Big ]^{-2}\)

= 129600

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

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

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

= \([ML^{-1}T^0]\)

Random error is reduced by making a large number of observations and taking mean of all the results.

(0.002) Maximum error in measuring mass = 0.001 g, because least count is 0.001 g, similarly, maximum error in measuring volume is 0.01 \(cm^3\)

\(\frac{\Delta p}{p} = \frac{\Delta M}{M} + \frac{\Delta V}{V}\)

\(= \frac{0.001}{20.000} + \frac{0.01}{10.00}\)

= \((5 \times 10^{-5}) + (1 \times 10^{-3})\)

= \(1.05 \times 10^{-3}\)

\(\Delta p = (1.05 \times 10^{-3}) \times p\)

= \(1.05 \times 10^{-3} \times \frac{20.000}{10.00}\)

= 0.002 g\(cm^{-3}\)

Light year measures distance and year measures time. One light year is the distance travelled by light in one year.