The gravitational force between two objects is $F$. How will this force change when:
$(i)$ the distance between them is reduced to half?
$(ii)$ the mass of one of the objects becomes four times?

The mass of a man on the earth is $100\, kg$. Does his weight on the moon increase or decrease?

$A$ soft drink bottle is dropped by a waiter from the top of a hotel whose height is $100 \, m$. It takes $T$ seconds to reach the ground. Where will it be at $T/2$ seconds?

State the source of centripetal force that our earth requires to revolve around the sun. List the factors on which this force depends.

$(a)$ Differentiate between $G$ and $g$.
$(b)$ Is the value of $g$ the same everywhere on Earth? Reason out.
$(c)$ How does the gravitational force between two objects change if the distance between them is tripled?

$(a)$ $A$ cube of side $5\, cm$ is immersed in water and then in a saturated salt solution. In which case will it experience a greater buoyant force? If each side of the cube is reduced to $4\, cm$ and then immersed in water,what will be the effect on the buoyant force experienced by the cube as compared to the first case for water? Give reasons for each case.
$(b)$ $A$ ball weighing $4\, kg$ with a density of $4000\, kg\, m^{-3}$ is completely immersed in water of density $10^3\, kg\, m^{-3}$. Find the force of buoyancy on it. (Given $g = 10\, m\, s^{-2}$)