At what point in its trajectory does a projectile have its $(i)$ maximum speed and $(ii)$ minimum speed?

Define the "universal law of gravitation".

Find the weight of an $80\, kg$ man on the surface of the moon. What would be his mass on the Earth and on the moon? $(g_{e} = 9.8\, m s^{-2}, g_{m} = 1.63\, m s^{-2})$

Suppose a planet exists whose mass and radius both are half that of Earth. Calculate the acceleration due to gravity on the surface of this planet.

$(a)$ What do you mean by acceleration due to gravity?
$(b)$ What is the value of $g$ on the surface of the earth?
$(c)$ On what factors does the value of $g$ depend?

$(i)$ How is the force of attraction dependent on the masses of objects and the distance between them?
$(ii)$ The mass of the Earth is $6 \times 10^{24} \, kg$ and that of a natural satellite is $6.5 \times 10^{20} \, kg$. If the distance between them is $3.35 \times 10^{6} \, km$, calculate the force exerted by the Earth on it. $(G = 6.7 \times 10^{-11} \, Nm^{2} kg^{-2})$