If Planck’s constant ($h$) and speed of light in vacuum ($c$) are taken as two fundamental quantities, which one of the following can, in addition, be taken to express length, mass and time in terms of the three chosen fundamental quantities?
Mass of electron ($m_e$)
Universal gravitational constant ($G$)
Charge of electron ($e$)
Mass of proton ($m_p$)
Which of the following ratios express pressure?
Force/Area
Energy/Volume
Energy/Area
Force/Volume
Which of the following are not a unit of time ?
Second
Parsec
Year
Light year
Why do we have different units for the same physical quantity?
The value of any given physical quantity may vary over a wide range, therefore, different units of the same physical quantity are required.
e.g., The length of a pen can be easily measured in cm, the height of a tree can be measured in metres, the distance between two cities can be measured in kilometres and distance between two heavenly bodies can be measured in light year.
The radius of atom is of the order of 1 Å and radius of nucleus is of the order of fermi. How many magnitudes higher is the volume of atom as compared to the volume of nucleus?
Radius of atom = 1Å = 10-10 m
Radius of nucleus = 1 fermi = 10-15 m
Volume of atom = Va = $\frac{4}{3}\pi R_{A}^{3}$
Volume of nucleus Vn = $\frac{4}{3}\pi R_{N}^{3}$
$\frac{V_{a}}{V_{n}}=\frac{\frac{4}{3}\pi R_{A}^{3}}{\frac{4}{3}\pi R_{N}^{3}}=\left(\frac{R_{A}}{R_{N}}\right)^{3} = \left(\frac{10^{-10}}{10^{-15}}\right)^{3} = 10^{15}$
Note: In such type of questions, always change the value in the same unit.