An object weighs $10 \, N$ in air. When immersed fully in water,it weighs only $8 \, N$. The weight of the liquid displaced by the object will be (in $, N$)

Two stones $A$ and $B$ are dropped from a multi-storey building. Stone $A$ is dropped from $100 \, m$ and at the same time stone $B$ is dropped from $50 \, m$ height. Both of them reach the earth at the same time. Will they have equal velocity while reaching the ground? Calculate and find out the answer (Take $g = 10 \, m s^{-2}$).

$A$ stone is dropped from the top of a tower. Its speed after it has fallen $20 \, m$ is (Take $g = 10 \, m s^{-2}$): (in $, m s^{-1}$)

$A$ ball is thrown up and attains a maximum height of $100 \, m$. It is thrown upwards with a speed of: (in $, m/s$)

$(a)$ Write the formula to find the magnitude of the gravitational force between the Earth and an object on the surface of the Earth.
$(b)$ What is the direction of acceleration due to gravity?

What is meant by acceleration due to gravity? Suppose a planet exists whose mass and radius both are half of that of Earth. Calculate the acceleration due to gravity on the surface of this planet.