Gravitation Tes...

Two point masses having mass $$m_1$$ and $$m_2$$ respectively. If the distance between two masses is increased by a factor of $$2$$. Then gravitational force:

A stone dropped from a height falls towards the earth because

Two objects have the same mass and are located near each other at a distance $$r$$. If the mass of one of the objects is doubled and the mass of the other object is tripled, find out the change in gravitational attraction between them?

Two planet of mass $$m$$ and $$100m$$. If gravitational force exerted by planet of mass $$100m$$ on the planet of mass $$m$$ is $$F_1$$ and gravitational force exerted by planet of mass $$m$$ on the planet of mass $$100m$$ is $$F_2$$. Then which of the following is true?

An astronaut visits another planet which has less gravitational acceleration than the earth. While on that planet, the astronaut will notice that his:

If the Earth were compressed in such a way that its mass remained the same, but the distance around the equator were just one-half what it is now, what would be the acceleration due to gravity at the surface of the Earth?

An astronaut stands on the top of a crater on the moon. He drops a rock from the top of the crater. Calculate the fraction of its speed to the final impact speed when it is midway between the top and bottom of the crater.

A purple ball rolls off a horizontal table with an initial speed of $$3.0 m/s$$. A red ball rolls off the same table with an initial speed of $$1.5 m/s$$. Both balls fly undhindered toward the horizontal floor that they hit at some horizontal distance from the edge of the table.
How does the horizontal distance for the purple ball compare to the horizontal distance for the red ball?

If  $$F$$ is the gravitational force between two objects of masses $${m}_{1}$$ and $${m}_{2}$$ separated by a distance $$R$$. Find out the new magnitude of the gravitational force between them if we double the distance between them ?

Rank the arrangements of masses given in the table below according the force between masses, greatest first.
The first column in the table tells the mass of one of the objects in each arrangements, the second column gives the mass of the second object , and the third column gives the distance between the centers of the objects.