$A$ box when hung from a spring balance shows a reading of $50 \,kg$. If the same box is hung from the same spring balance inside an evacuated chamber,the reading on the scale will be

$A$ metal cube is embedded inside a block of ice that is floating on the surface of water. The ice melts completely, and the metal cube sinks into the water. What happens to the water level in the container?

The reading of a spring balance when a block is suspended from it in air is $60 \, N$. This reading is changed to $40 \, N$ when the block is submerged in water. The specific gravity of the block must be therefore ............

$A$ hot air balloon is carrying some passengers and a few sandbags of mass $1 kg$ each,so that its total mass is $480 kg$. Its effective volume providing buoyancy is $V$. The balloon is floating at an equilibrium height of $100 m$. When $N$ number of sandbags are thrown out,the balloon rises to a new equilibrium height of $150 m$ with its volume $V$ remaining unchanged. If the variation of the density of air with height $h$ from the ground is $\rho(h) = \rho_0 e^{-\frac{h}{h_0}}$,where $\rho_0 = 1.25 kg m^{-3}$ and $h_0 = 6000 m$,the value of $N$ is:

$A$ 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 $Cu = 8.8\, g/cc$.

$A$ block of ice floats on a liquid of density $1.2 \ g/cm^3$ in a beaker. What happens to the level of the liquid when the ice completely melts?