Write True or False for the following statement:
The value of $G$ is high if the radius of the body is more and less if radius is less.

When an object, say an apple, falls towards the Earth, the Earth rises up to meet it. Is this true? If so, why is the Earth's motion not noticeable?

$(a)$ The Earth is acted upon by the gravitation of the Sun,yet it does not fall into the Sun. Why?
$(b)$ An object of mass $500 \, g$ is dropped from a tower of height $5 \, m$. Calculate its momentum when it touches the ground (given $g = 10 \, m s^{-2}$).

An object has a mass of $30 \ kg$. What is its weight $(i)$ on the moon $(ii)$ on another planet? The value of $g$ on the moon is $1/6$ the value of $g$ on the earth. The value of $g$ on the planet is $3$ times the value of $g$ on the earth. Take $g_{earth} = 10 \ m/s^2$.

$A$ man throws a ball of mass $0.5 \, kg$ vertically upward with a velocity of $25 \, m s^{-1}$. Find: $(a)$ the initial momentum of the ball,$(b)$ the momentum of the ball at the halfway mark of the maximum height. (Given $g = 10 \, m s^{-2}$)

State the universal law of gravitation. How is the force between two bodies affected if the distance between them is tripled?