Two identical balls each have a mass of 10 g. What charges should these balls be given so that their interaction equalizes the force of universal gravitation acting between them? The radii of the balls may be ignored in comparison to distance between them.

Question

Two identical balls each have a mass of 10 g. What charges should these balls be given so that their interaction equalizes the force of universal gravitation acting between them? The radii of the balls may be ignored in comparison to distance between them. (A) 6.34 × 10-11 C (B) 8.57 × 10-11 C (C) 6.34 × 10-13 C (D) 8.57 × 10-13 C

Tardigrade Admin · Accepted Answer

If q charge is given to each ball, then (1/4 π ε0) ⋅ (q × q/r2)=G (m × m/r2) Or q=√4 π ε0 G × m Setting G=6.6 × 10-11 Nm 2 kg -2 and m=10 g =10 × 10-3 kg, we get q=8.57 × 10-13 C

Q. Two identical balls each have a mass of $10 g$ . What charges should these balls be given so that their interaction equalizes the force of universal gravitation acting between them? The radii of the balls may be ignored in comparison to distance between them.

$6.34 \times 1 0^{- 11} C$

$8.57 \times 1 0^{- 11} C$

$6.34 \times 1 0^{- 13} C$

$8.57 \times 1 0^{- 13} C$

If $q$ charge is given to each ball, then
$\frac{1}{4 π ε _{0}} \cdot \frac{q \times q}{r ^{2}} = G \frac{m \times m}{r ^{2}}$
Or $q = 4 π ε_{0} G \times m$
Setting $G = 6.6 \times 1 0^{- 11} N m^{2} k g^{- 2}$ and
$m = 10 g = 10 \times 1 0^{- 3} k g$ , we get
$q = 8.57 \times 1 0^{- 13} C$

Q. Two identical balls each have a mass of 10g. What charges should these balls be given so that their interaction equalizes the force of universal gravitation acting between them? The radii of the balls may be ignored in comparison to distance between them.

6.34×10−11C

8.57×10−11C

6.34×10−13C

8.57×10−13C