Question

Two coins, made of different material, are placed next to each other so that they are touching. Both coins are 15mm in diameter. One coin has a mass of 6.5 g and the gravitational force between the coins is 4.03 × 10^-11 N

Answer 1

The mass of the second coin for the given gravitation force is 20.9 g.

The given parameters;

• distance between the two coins, r = 15 mm = 0.015 m
• mass of one coin, m₁ = 6.5 g = 0.0065 kg
• gravitational force between the coins =  4.03 × 10⁻¹¹ N

The mass of the second coin is determined by applying Newton's law of universal gravitation as shown below;

$F = \frac{Gm_1 m_2 }{R^2} \\\\m_2 = \frac{FR^2}{Gm_1} \\\\m_2 = \frac{(4.03 \times 10^{-11}) \times (0.015)^2}{(6.67 \times 10^{-11}) \times (0.0065)} \\\\m_2 = 0.0209 \ kg\\\\m_2 = 20.9 \ g$

Thus, the mass of the second coin for the given gravitation force is 20.9 g.

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