Answer:
A) q = 5.714 × 10^(13) C
B) Because from a above, F_e = F_g and so r² canceled out in the formulas
C) m_t = 5.964 × 10⁴ kg
Explanation:
For the gravitational attraction of the earth and moon to be neutralized, the electrostatic force must be equal to the gravitational force i.e F_e = F_g
Now, F_e = kq²/r² and F_g = GmM/r²
Equating them and making q the subject, we arrive at;
q = √(GmM/k)
Where;
G is gravitational constant = 6.67 × 10^(-11) m³/kg.s²
m is mass of moon = 7.36 × 10^(22) kg
M is mass of earth = 5.98 × 10^(24) kg
k is coulombs constant = 8.99 x 10^(9) N.m²/c²
q = √(6.67 × 10^(-11) × 7.36 × 10^(22) × 5.98 × 10^(24)/8.99 x 10^(9))
q = 5.714 × 10^(13) C
B) We don't need the lunar distance because from a above, F_e = F_g and so r² canceled out in the formulas.
C) The number of protons is given by the formula;
n = q/e
Where, e is charge of the proton = 1.6 × 10^(-19) C
n = (5.714 × 10^(13))/(1.6 × 10^(-19))
n = 3.57125 × 10^(32)
Total mass of these protons is given by the formula;
m_t = nm_p
Where m_p is mass of a single proton = 1.67 × 10^(-27) kg
m_t = 3.57125 × 10^(32) × 1.67 × 10^(-27)
m_t = 5.964 × 10⁴ kg
