$A$ solid cube is floating in a liquid. The coefficient of linear expansion of the cube is $\alpha$ and the coefficient of volume expansion of the liquid is $\gamma$. On increasing the temperature of the (liquid + cube) system,the cube will sink if

$A$ hollow sphere of mass $M$ and radius $R$ is immersed in a tank of water (density $\rho_w$). The sphere would float if it were set free. The sphere is tied to the bottom of the tank by two wires which make an angle of $45^{\circ}$ with the horizontal as shown in the figure. The tension $T_1$ in each wire is:

$A$ leak-proof cylinder of length $1 \; m,$ made of a metal which has a very low coefficient of expansion,is floating vertically in water at $0^{\circ} C$ such that its height above the water surface is $20 \; cm.$ When the temperature of water is increased to $4^{\circ} C,$ the height of the cylinder above the water surface becomes $21 \; cm.$ The density of water at $T=4^{\circ} C,$ relative to the density at $T=0^{\circ} C,$ is close to

$A$ sample of metal weighs $210 \ g$ in air,$180 \ g$ in water,and $120 \ g$ in a liquid. Then,the relative density $(RD)$ of:

$A$ wooden block floating in a bucket of water has $\frac{4}{5}$ 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 half in oil. The density of oil relative to that of water is

$A$ body of density $\rho$ is dropped from rest at a height $h$ into a lake of density $\delta$ $(\delta > \rho)$. Neglecting all dissipative forces,find the maximum depth to which the body sinks before returning to float on the surface.