Question

A 4.8 g object carries 3.2 μC . It acquires a speed v when accelerated from rest through a potential difference V.

If a 2.0 g object acquires twice the speed under the same circumstances, what’s its charge?

Express your answer using two significant figures.

Answer 1

m = mass = 4.8 g = 0.0048 kg

q = charge = 3.2 x 10^-6 C

V₁ = initial Potential difference = V

v₁ = speed = v

Using conservation of energy ,

Electric potential energy lost = Kinetic energy gained

qV = (0.5) m v²                                        Eq-1

Case 2 :

m' = mass = 2 g = 0.002 kg

q' = charge = ?

V₂ = initial Potential difference = V

v₂ = speed = 2v

Using conservation of energy ,

Electric potential energy lost = Kinetic energy gained

q'V = (0.5) m' (2v)²                          Eq-2            

Dividing Eq-1 by Eq-2

q/q' = (m/m') (1/4)

(3.2 /q') = (4.8/2) (0.25)

(3.2 /q') = 0.6

q' = 5.33 uC