A slender homogeneous rod of length $2L$ floats partly immersed in water, being supported by a string fastened to one of its ends, as shown. The specific gravity of the rod is $0.75$. The length of rod that extends out of water is : 

A vessel contains oil (density =$ 0.8 \;gm/cm^3$) over mercury (density = $13.6\; gm/cm^3$). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in $ gm/cm^3$ is

A wooden block floating in a bucket of water has $\frac{4}{5}$ of its volume submerged. When certain amount of an 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 half in oil. The density of oil relative to that of water is

A cubical block of side $0.5\,m$ floats on water with $30\%$ of its volume under water. ……. $kg$ is the maximum weight that can be put on the block without fully submerging it under water ? [Take density of water $= 10^3\,kg/m^3$ ]

A vessel containing water is given a constant acceleration a towards the right, along a straight horizontal path. Which of the following diagram represents the surface of the liquid