Column I

(A) GM_eM_s ,
G $$ \to $$ universal gravitational constant, M_e $$ \to $$ mass of the earth, M_s $$ \to $$ mass of the Sun

(B) $${{3RT} \over M}$$,
R $$ \to $$ universal gas constant, T $$ \to $$ absolute temperature, M $$ \to $$ molar mass

(C) $${{{F^2}} \over {{q^2}{B^2}}}$$ ,
F $$ \to $$ force, q $$ \to $$ charge, B $$ \to $$ magnetic field

(D) $${{G{M_e}} \over {{R_e}}}$$,
G $$ \to $$ universal gravitational constant, M_e $$ \to $$ mass of the earth, R_e $$ \to $$ radius of the earth

Column II

(p) (volt) (coulomb) (metre)

(q) (kilogram) (metre)³ (second)⁻²

(r) (meter)²(second)⁻²

(s) (farad) (volt)² (kg)⁻¹

A temperature difference can generate e.m.f. in some materials. Let S be the e.m.f. produced per unit temperature difference between the ends of a wire, σ the electrical conductivity and κ the thermal conductivity of the material of the wire. Taking M, L, T, I and K as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $Z = \frac{S^2 \sigma}{\kappa}$ is :

Figure 1 shows the configuration of main scale and Vernier scale before measurement. Fig. 2 shows the configuration corresponding to the measurement of diameter D of a tube. The measured value of D is:

A dimensionless quantity is constructed in terms of electronic charge $e$, permittivity of free space $\varepsilon_0$, Planck's constant $h$, and speed of light $c$. If the dimensionless quantity is written as $e^\alpha \varepsilon_0{ }^\beta h^\gamma c^\delta$ and $n$ is a non-zero integer, then $(\alpha, \beta, \gamma, \delta)$ is given by :