$A$ 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:

$Assertion :$ The buoyant force on a submerged rigid object can be considered to be acting at the centre of mass of the object.
$Reason :$ For a rigid body,a force field distributed uniformly through its volume can be considered to be acting at the centre of mass of the body.

$A$ 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 ............

An ice cube contains a large air bubble. The cube is floating on the horizontal surface of water contained in a trough. What will happen to the water level when the cube melts?

$A$ solid sphere of radius $R$ and density $\rho$ is attached to one end of a massless spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3\rho$. The complete arrangement is placed in a liquid of density $2\rho$ and is allowed to reach equilibrium. The correct statement$(s)$ is (are):
$(A)$ The net elongation of the spring is $\frac{4 \pi R^3 \rho g}{3 k}$
$(B)$ The net elongation of the spring is $\frac{8 \pi R^3 \rho g}{3 k}$
$(C)$ The light sphere is partially submerged.
$(D)$ The light sphere is completely submerged.

What is buoyancy?