Question

Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II.

Column I	Column II
i. $G{M}_e{M}_s$	a. (volt) (coulomb) (metre)
ii. $3RT/M$	b. $\left(kilogram\right)\left(metre{)}^3\right(second{)}^2$
iii. $F^2/q^2{B}^2$	c. $\left(meter{)}^2\right(second{)}^{-2}$
iv. $G{M}_e/R_e$	d. $\left(farad\right)\left(volt{)}^2\right(kg{)}^{-1}$

where G is universal gravitational constant; $M_e$ mass of the earth; $M_s$, mass of sun; $R_e$ radius of the earth; R, universal gas constant;T, absolute temperature; M, molar mass, F, force; q, charge; B, magnetic field.

• A. $i\to b.,ii\to c.,d.,iii\to c.,d.,iv\to c.,d.,$
• B. $i\to a.,ii\to c.,d.,iii\to c.,d.,iv\to c.,d.,$
• C. $i\to d.,ii\to c.,d.,iii\to c.,d.,iv\to c.,d.,$
• D. $i\to c.,ii\to c.,b.,iii\to c.,d.,iv\to c.,d.,$

Answer 1

Answer: (B)

$i\to a.,ii\to c.,d.,iii\to c.,d.,iv\to c.,d.,$

$G{M}_e{M}_s=F{r}^2=N{m}^{2}kg\frac{m}{s^2}\times m^2=kg{m}^3{s}^{-2}$

Also : (volt) (coulomb) (metre) $N{m}^2$

$v_{rms}=\sqrt{\frac{3RT}{M}}\Rightarrow v_{rms}^2=\frac{3RT}{M}$

Unit of $\frac{3RT}{M}$ is $m^2{s}^{-2}$

Also (farad) $\left(volt{)}^2\right(kg{)}^{-1}=m^2{s}^{-2}$

$F=qvB\Rightarrow v^2=\frac{F^2}{q^2{B}^{\prime 2}}$

Hence, unit of $v^2$ is $m^2{s}^{-2}$ which is further equal to $FVk{g}^{-1}$

Escape velocity, $V_e=\sqrt{\frac{2GM}{R}}\Rightarrow V_e^2=\frac{2GM}{R}$

So the unit of $\frac{GM}{R}$ is $m^2{s}^{-2}$

After comparing from column-II

$i\to a.,ii\to c.,d.,iii\to c.,d.,iv\to c.,d.,$