Question

Two identical 9.10-g metal spheres (small enough to be treated as particles) are hung from separate 300-mm strings attached to the same nail in a 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 a 13.0 ∘ angle with the vertical. How many surplus electrons are on each sphere?

Answer 1

`n = 1.266* 10^(12)`

Step-by-step explanation:

Given data:

mass of sphere is 10 g

Angle between string and vertical axis is
`\theta = 13 degree`

thickness of string 300 mm = 0.3 m

`sin\theta =(2)/(0.3 m)`

r =0.3 sin 13 = 0.067 m

`Fe = ( kq_1 q-2)/(d^2)`

`Fe = (kq^2)/((2r)^2) = mg tan\theta`

`q^2 =  mg tan\theta ((2r)^2)/(k)`

`= 0.0091 * 9.8 tan13 * ((2* 0.067)^2)/(9* 10^9)`

`q^2 = 4.10* 10^(-14)`

`q = 2.026 * 10^(-7) C`

q = ne

`n = (1.6* 10^(-19))/(2.02* 10^(-7))`

`n = 1.266* 10^(12)`