$A$ wooden block with a coin placed on its top floats in water as shown in the figure. $l$ and $h$ are as shown. After some time,the coin falls into the water. Then:

$A$ log of wood of mass $120 \ kg$ floats in water. The mass that can be put on the raft to make it just sink should be ....... $kg$ (density of wood = $600 \ kg/m^3$,density of water = $1000 \ kg/m^3$).

If there were a smaller gravitational effect,which of the following forces do you think would alter in some respect?

$A$ hollow spherical body of outer and inner radii of $4 \ cm$ and $2 \ cm$ respectively floats half submerged in a liquid of density $2.0 \ g \ cm^{-3}$. The density of the material of the sphere is (in $g \ cm^{-3}$)

An object weighs $m_1$ in a liquid of density $d_1$ and $m_2$ in a liquid of density $d_2$. The density $d$ of the object is

$A$ 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.