$A$ boat carrying a number of stones is floating in a water tank. If the stones are unloaded into the water,the water level in the tank will ............

$A$ wooden piece floats half-submerged in a tub of water. If the system is transferred to a lift ascending with acceleration $a$,the wooden piece will:

$A$ weightless bag is filled with $5 \,kg$ of water and is weighed in water using a spring balance. The reading of the spring balance is (in $\,kg$)

$A$ container of liquid is in free fall. Without any liquid spilling out, does this container obey the principle of Archimedes?

State the law of floatation and describe its cases.

$A$ hemispherical portion of radius $R$ is removed from the bottom of a cylinder of radius $R$. The volume of the remaining cylinder is $V$ and its mass is $M$. It is suspended by a string in a liquid of density $\rho$ where it stays vertical. The upper surface of the cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the liquid is