Question

The gravitational force is thrice as great on a 3 kg rock as on a 1 kg rock. What should you do so that the 3 kg will not fall with thrice the acceleration as that of the 1 kg rock?

Answer 1

If the gravitational force is directly proportional to the mass, the aceleration should be inversly proportional to the mass, in order the 3 kg will not fall with thrice the acceleration as that of the 1 kg rock. And it is true, since the second Newton's law holds:

$$a = \dfrac{F}{m}$$

Let $F_1, m_1 = 1kg$ be the gravitational force and mass of the first rock respectively. Then $F_2 = 3F_1, m_2 = 3m_1$ are the gravitational force and mass of the second rock respectively. Then the accleleration of the first rock is:

$$a_1 = \dfrac{F_1}{m_1}$$

And the acceleration of the secon force is:

$$a_2 = \dfrac{F_2}{m_2} = \dfrac{3F_1}{3m_1} = \dfrac{F_1}{m_1} = a_1$$

Thus, both accelerations are equal.

Answer. The aceleration should be inversly proportional to the mass.