$A$ small solid ball is dropped from a height above the free surface of a liquid. It strikes the surface of the liquid at $t = 0$. The density of the material of the ball is $500 \ kg/m^3$ and that of the liquid is $1000 \ kg/m^3$. If the ball comes momentarily to rest at $t = 2 \ s$,then the initial height of the ball from the surface of the liquid was ..... $m$ (neglect viscosity).

$A$ $20 \,g$ copper block is suspended by a vertical spring causing $1 \,cm$ elongation over the natural length of the spring. If a beaker of water is placed below the block so that the copper block is completely immersed in the liquid, the elongation of the spring is (Density of copper = $9000 \,kg/m^3$, Density of water = $1000 \,kg/m^3$, $g = 10 \,m/s^2$) (in $\,cm$)

$A$ wooden piece floats half-submerged in a tub of water. If the system is transferred to a lift ascending with acceleration $a$,the wooden piece will:

$A$ body of density $\rho$ is dropped from rest at a height $h$ into a lake of density $\sigma$ $(\sigma > \rho)$. The maximum depth to which the body sinks before returning to float on the surface is (neglect air dissipative forces).

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:

$A$ small wooden ball of density $\rho$ is immersed in water of density $\sigma$ to a depth $h$ and then released. The height $H$ above the surface of water up to which the ball will jump out of water is