ssume that you are way out in space, very very far away from other masses, and you have two identical particles each of which has the charge of an electron. Suppose you hold both of these particles 0.1m apart from each other and then release them. What mass would these particles have to have in order for the gravitational force to exactly balance the electric force? (So that they don't move.) [Put units on all numbers.]
Assume that you are way out in space, very very far away from other masses, and you have two identical particles
each of which has the charge of an electron. Suppose you hold both of these particles 0.1m apart from each other and then release them. What mass would these particles have to have in order for the gravitational force to exactly balance the electric force? (So that they don't move.) [Put units on all numbers.]
Let the mass of each particle is m kg.
Now, electric force = K (Q1) .(Q2)/(0.1)^2
Gravity force = G (m) (m) /(0.1)^2
For equilibrium, both force must be equal.
K (e^2) /(0.1)^2 = G . (m^2) /(0.1)^2
K . e^2 = G. m^2
Or ,
m^2 = (K/G) .e^2
m = (K/G) ^0.5 × e
Now, K = 9 × 10^9 N m^2 C^-2
G = 6.67 × 10^-11 m^3 kg^-1 s^-2
All are is SI units.
(K/G)^0.5 =( 9/6.67)^0.5 ×( 10^20)^0.5 = 1.1616 × 10^10 kg C^-1.
Mass m = 1.1616 × 10^10 × e = 1.1616 × 10^10 × 1.6 × 10^-19 C . Kg. C^-1
Hence m = 1.86 × 10^-9 Kg.
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