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 $g_{earth} = 10 \ m/s^2$.

State the universal law of gravitation. Write the $SI$ unit of $G$. The gravitational force between two objects is $100 \, N$. How should the distance between the objects be changed so that the force between them becomes $50 \, N$?

$A$ stone is released from the top of a tower of height $19.6 \, m$. Calculate its velocity just before touching the ground.

$(a)$ $A$ 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 $g = 10\, m\, s^{-2}$)

If the density of a planet is doubled without changing its radius,how does $g$ on the planet change?

Show that if the earth attracts two bodies $A$ and $B$ placed at the same distance from the centre of the earth with the same force,then their masses are equal.