The atmosphere is held to the earth by

$A$ 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?

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

Consider Earth to be a homogeneous sphere. Scientist $A$ goes deep down in a mine and scientist $B$ goes high up in a balloon. The acceleration due to gravity as measured by:

Find the weight of an $80\, kg$ man on the surface of the moon. What would be his mass on the Earth and on the moon? $(g_{e} = 9.8\, m s^{-2}, g_{m} = 1.63\, m s^{-2})$

$(i)$ Seema buys a few grains of gold at the poles as per the instructions of one of her friends. She hands over the same when she meets her at the equator. Will the friend agree with the weight of gold bought? If not,why?
$(ii)$ If the moon attracts the earth,why does the earth not move towards the moon?