Question

G a small metal sphere, carrying a net charge is held stationary. what is the speed are 0.4 m apart

Answer 1

The final speed of small metal sphere is 12.6 m/s.

Step-by-step explanation:

Given that,

Distance = 0.4 m

Suppose, A small metal sphere, carrying a net charge q₁ = −2μC, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q₂ = −8μC and mass 1.50g, is projected toward q₁. When the two spheres are 0.800m apart, q₂ is moving toward q₁ with speed 20m/s.

We need to calculate the final speed of small metal sphere

Using conservation of energy

`(1)/(2)mv_(1)^2+(kq_(1)q_(2))/(r_(1))=(1)/(2)mv_(2)^2+(kq_(1)q_(2))/(r_(2))`

`(1)/(2)m(v_(1)^2-v_(2)^2)=kq_(1)q_(2)((1)/(r_(2))-(1)/(r_(1)))`

Put the value into the formula

`(1)/(2)*1.5*10^(-3)(20^2-v_(2)^2)=9*10^(9)*(-2)*10^(-6)*(-8)*10^(-6)((1)/(0.4)-(1)/(0.8))`

`400-v_(2)^2=240`

`-v_(2)^2=240-400`

`v_(2)=√(160)\ m/s`

`v_(2)=12.6\ m/s`

Hence, The final speed of small metal sphere is 12.6 m/s.