LASER stands for 'Light Amplification by Stimulated Emission of Radiation'.

1 micron (1\(\mu \) ) = 10^-6 m
1 nanometre (1 nm) = 10^-9 m

 About 1 in 10¹² to 10¹³ s.

1 a.m.u. = \(\frac{1}{12}\) th mass of carbon-12 atom, i.e., 1.66 x 10^-27 kg.

Units of those physical quantities which are derived from the fundamental units are called derived units.

The relation is given as \({ \nu }^{ 2 }-{ u }^{ 2 }=2as\)
On LHS Dimension of \({ \nu }^{ 2 }=\left[ { L }^{ 2 }T^{ -2 } \right]\)
\( \\ { u }^{ 2 }=\left[ { L }T^{ -1 } \right] ^{ 2 }=\left[ { L }^{ 2 }{ T }^{ -2 } \right] \)
RHS 2 as = \(\left[ LT^{ -2 } \right] \left[ L \right] =\left[ { L }^{ 2 }{ T }^{ -2 } \right] \)
As dimensions of both terms on LHS are equal to the dimensions of RHS, the relation is dimensionally correct.

As \(x=a+bt+c{ t }^{ 2 }\), where x in metre and t in second. Hence, in accordance with the principle of homogeneity of dimensions, we have
Unit of a = x = metre
Unit of b = unit of \(\frac { x }{ t } \) = \({ m }/{ s }\) and
Unit of c = unit of \(\frac { x }{ { t }^{ 2 } } \) = \({ m }/{ (s) }^{ 2 }\) 

4 g, 4 cm,0.4

5.67 x 10^-8 Js^-1m^-2K^-4

Since, F = kν²
Hence, \( [k]=\frac { [F] }{ [\nu ^{ 2 }] } \)
\(\\ =\frac { [MLT^{ -2 }] }{ [LT^{ -1 }]^{ 2 } } = [{ M }^{ 1 }L^{ -1 }]\) 

27657.1 mm²

Both bar and torr are the units of pressure.
1 bar = 1 atmospheric pressure = 760 mm of Hg column
= 10⁵N/m²
1 torr = 1mm of Hg column
1 bar = 760 torr

\(\frac { \triangle x }{ x } =\frac { 0.01 }{ 40.00 } =0.00025\)

Acceleration = (10 m/(1s)²) 
= (10 x 10^-3 / [1/60 x 60])²
= (3600)² x 10^-2 km/h²
= 1.29 x 10⁵ km/h².

The speed of light (c) = 1 new unit of length s^-1
Time taken by light to reach the earth t = 8 min + 20 s = (8 x 60 x 20) s = 500 s
Distance between the sun and the earth  = speed of light X time
x = c x t = 1 new unit of length s^-1 x 500 s
= 500 new unit of length