Question

g Two identical metal spheres (small enough to be treated as particles) each with a mass of 3.1 × 10−3 kg are hung from separate identical strings. The strings are 0.70 m long and are attached to the same nail in the ceiling. Surplus electrons are added to each sphere, and then the spheres are brought in contact with each other and released. Their equilibrium position is such that each string makes an angle of 15.0° with the vertical. How many surplus electrons are on each sphere?

Answer 1

Step-by-step explanation:

Let q be the charges on each spheres , 2d be the distance between them in equilibrium , T be tension in the string and F be the force of repulsion between them

F = k q² /4d²

For equilibrium

T sin15 = F

T cos 15 = mg

tan15 = F / mg

F = mg tan15

k q² /4d² = mg tan15

k q² = 4d² x mg tan15

= 4 x( .7 sin15)² x 3.1 x 10⁻³ x 9.8 x .2679

= 1.068 x 10⁻³

q = .3444 x 10⁻⁶ C

no of electrons

= .3444 x 10⁻⁶ / 1.6 x 10⁻¹⁹

= 215.25 x 10¹⁰