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 EI, EII and EIII 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
(A) GMeMs ,
G $$ \to $$ universal gravitational constant, Me $$ \to $$ mass of the earth,
Ms $$ \to $$ 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,
Me $$ \to $$ mass of the earth, Re $$ \to $$ 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 student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of $$\pm0.05\;\mathrm{mm}$$ at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of $$\pm0.01\;\mathrm{mm}$$. Take g = 9.8 m/s2 (exact). The Young's modulus obtained from the reading is