$A$ block of iron contains a hollow cavity as shown below. The block weighs $6000 \,N$ in air and $4000 \,N$ in water. If the densities of iron and water are $6 \,g/cm^3$ and $1 \,g/cm^3$ respectively, then the volume of the cavity is (assume $g = 10 \,m/s^2$): (in $\,m^3$)

$A$ sphere of relative density $\sigma$ and diameter $D$ has a concentric cavity of diameter $d$. The ratio of $\frac{D}{d}$,if it just floats on water in a tank,is:

$Assertion$ : $A$ balloon filled with hydrogen will fall with acceleration $\frac{g}{6}$ on the moon.
$Reason$ : Moon has no atmosphere.

An object with uniform density $\rho$ is attached to a spring that is known to stretch linearly with applied force. When the spring-object system is immersed in a liquid of density $\rho_1$,the spring stretches by an amount $x_1$ (where $\rho > \rho_1$). When the experiment is repeated in a liquid of density $\rho_2$ (where $\rho_2 < \rho_1$),the spring stretches by an amount $x_2$. Neglecting any buoyant force on the spring,the density of the object is:

$A$ 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:

Two solid pieces,one of steel and the other of aluminium,when immersed completely in water,have equal weights. When the solid pieces are weighed in air: