$A$ cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with a net acceleration of $g/3$,the fraction of volume immersed in the liquid will be:

$A$ body floats in a liquid contained in a beaker. The whole system,as shown,falls freely under gravity. The upthrust on the body due to the liquid is

$Assertion :$ 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.

$A$ pan balance has a container of water with an overflow spout on the right-hand pan as shown. It is full of water right up to the overflow spout. $A$ container on the left-hand pan is positioned to catch any water that overflows. The entire apparatus is adjusted so that it is balanced. $A$ brass weight on the end of a string is then lowered into the water,but not allowed to rest on the bottom of the container. What happens next?

$A$ block of wood floats in water with $\frac{4}{5}$ of its volume submerged,but it just floats in another liquid. The density of the liquid is (in $kg/m^3$):

$A$ wooden block floating in a bucket of water has $(4/5)$th of its volume submerged. When a certain amount of oil is poured into the bucket,it is found that the block is just under the oil surface,with half of its volume under water and the other half in oil. The density of oil relative to that of water is