$A$ weightless bag is filled with $5 \,kg$ of water and is weighed in water using a spring balance. The reading of the spring balance is (in $\,kg$)

$A$ solid cube is floating in a liquid. The coefficient of linear expansion of the cube is $\alpha$ and the coefficient of volume expansion of the liquid is $\gamma$. On increasing the temperature of the (liquid + cube) system,the cube will sink if

An iceberg floats in water with part of it submerged. What is the fraction of the volume of the iceberg submerged,if the density of ice is $\rho_{i} = 0.917 \ g \ cm^{-3}$ and the density of water is $\rho_{w} = 1.00 \ g \ cm^{-3}$?

$A$ pendulum has a time period $T$ in air. When it is made to oscillate in water,it acquires a time period $T' = \sqrt{2} T$. The density of the pendulum bob is (density of water $= 1$)

$A$ piece of copper having an internal cavity weighs $264\, g$ in air and $221\, g$ in water. Find the volume (in $cc$) of the cavity. Density of $Cu = 8.8\, g/cc$.

$A$ body having volume $V$ and density $\rho$ is attached to the bottom of a container as shown. The density of the liquid is $d$ (where $d > \rho$). The container has a constant upward acceleration $a$. The tension in the string is: