At some place on the equator,a bag of sugar weighs $W \ kg$. Will it weigh the same,more,or less when taken to Antarctica? Give a reason for your answer.

Gravitational force on an imaginary planet is six times stronger than the gravitational force of the Earth. Determine the value of acceleration due to gravity and the weight of an object of mass $50 \, kg$ on that planet.

If gravitation is the power by which all bodies tend towards each other,then why do all bodies tend towards the centre of the earth?

The atmosphere is held to the earth by

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

$(i)$ Is the acceleration due to gravity of earth '$g$' always a constant at every place? Discuss.
$(ii)$ During a free fall,will heavier objects accelerate more than lighter ones? Give reason for your answer.