$A$ cylindrical block of wood of base area $30 \, cm^2$ floats in a liquid of density $900 \, kg/m^3$. The block is depressed lightly and then released. The time period of the resulting oscillations of the block is equal to that of a spring with a block of the same mass. The spring constant is equal to ........ $N/m$.

The fraction of a floating object of volume $V_0$ and density $d_0$ above the surface of a liquid of density $d$ will be

Two bodies having volumes $V$ and $2V$ are suspended from the two arms of a common balance and they are found to balance each other. If the larger body is immersed in oil (density $d_1 = 0.9 \ gm/cm^3$) and the smaller body is immersed in an unknown liquid,the balance remains in equilibrium. The density of the unknown liquid is given by ......... $gm/cm^3$.

An ice block floats in a liquid whose density is less than water. $A$ part of the block is outside the liquid. When the whole of the ice has melted,the liquid level will

$A$ 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:

$A$ piece of granite floats at the interface of mercury and water contained in a beaker as shown in the figure. If the densities of granite,water,and mercury are $\rho, \rho_1$,and $\rho_2$ respectively,the ratio of the volume of granite in water to the volume of granite in mercury is: