An ornament weighs $10\, g$ in air and $6\, g$ in water. The density of the material of the ornament is $20\, g/cc$. The volume of the cavity in the ornament is ........ $cc$.

The weight of an empty balloon on a spring balance is $w_1$. The weight becomes $w_2$ when the balloon is filled with air. Let the weight of the air itself be $w$. Neglect the thickness of the balloon when it is filled with air. Also,neglect the difference in the densities of air inside and outside the balloon. Then:

$A$ solid sphere of density $\rho_s$ which is $\eta$ $( > 1)$ times lighter than water (density $\rho_w$) is suspended in a water tank by a string tied to its base as shown in the figure. If the mass of the sphere is $m$,then the tension in the string is given by:

$A$ 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:

$A$ candle of diameter $d$ is floating on a liquid in a cylindrical container of diameter $D$ $(D >> d)$ as shown in the figure. If it is burning at the rate of $2 \text{ cm/hour}$,then the top of the candle will:

$A$ 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: