Universal Law of Gravitation

The value of Universal Gravitational Constant is 

The distance between the earth and the moon is

An apple falls from a tree. An insect in the apple finds that the earth is falling towards it with and acceleration $\text{'}g\text{'}$. Who exerts the force needed to accelerate the earth with this acceleration?

Can you think of two particles which do not exert gravitational force on each other? Why?

A ball is dropped from a height. If it takes $0.2 \mathrm{s}$ to cross the last $6 \mathrm{m}$ before hitting the ground, find the height from which it is dropped. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

Find the free-fall acceleration of an object on the surface of the moon, if the radius of the moon and its mass are $1740 \mathrm{km}$ and $7.4\times {10}^{22} \mathrm{kg}$ respectively. Compare this value with free-fall acceleration of a body on the surface of the earth.

Two spherical balls of mass $10 \mathrm{kg}$ each are placed with their centres $10 \mathrm{cm}$ apart. Find the gravitational force of attraction between them.

A ball is projected vertically up with a speed of $50 \mathrm{m} {\mathrm{s}}^{-1}$. Find the maximum height, the time to reach the maximum height and the speed at the maximum height. ($g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

What is the speed of an apple dropped from a tree after $1.5$ second? What distance will it cover during this time? Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

Explain universal law of gravitation.

Calculate the acceleration of the moon towards the earth's centre.