1The gravitational force between the Earth and a sphere of mass 1 kg is 9.8 N, and this force acts on both objects. Yet when the ball is dropped from a height, the Earth does not move upwards; only the ball appears to fall. Why? Using Newton's second law of motion, calculate the acceleration produced by this force on the 1 kg sphere and on the Earth of mass \( 5.97 \times 10^{24} \) kg.
2In the simulation activity, the force between a 300 kg and a 400 kg sphere 4 m apart is 0.000000500556 N. What conclusions can be drawn when (a) both masses are doubled to 600 kg and 800 kg, giving 0.000002002224 N, and (b) the distance is doubled to 8 m, giving 0.000000125139 N?
3State Newton's universal law of gravitation and derive the formula \( F = \frac{G m_1 m_2}{d^2} \).
4What is the universal gravitational constant? Give its value and SI unit, and explain why it is called universal.
5Two students, each of mass 50 kg, sit so that their centres are 1 m apart. Calculate the gravitational force between them. Why do they not feel it?
6The mass of one of two objects is made three times larger and the distance between them is halved. How many times does the gravitational force change?
7The Sun is far more massive than the Moon. Why, then, is the Moon's gravitation important for tides on the Earth?
8Write three consequences of gravitational force.
9In calculating the force between the Earth and a ball on its surface, why is the radius of the Earth used as d, and why must it be changed from km to m?