Student I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different length of the pendulum and/or record time for different number of oscillations. The observations area shown in the table.

Least count for length = 0.1 cm

Least count for time = 0.1 s

Student | Length of the pendulum (cm) |
No. of oscillations (n) |
Total time for(n) oscillations (s) |
Time periods (s) |
---|---|---|---|---|

I | 64.0 | 8 | 128.0 | 16.0 |

II | 64.0 | 4 | 64.0 | 16.0 |

III | 20.0 | 4 | 36.0 | 9.0 |

If E_{I}, E_{II} and E_{III} are the percentage errors in g, i.e., $$\left(\frac{\triangle g}g\times100\right)$$ for students I, II and III, respectively,then

**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**

(A) GM_{e}M_{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}