$A$ cork is submerged in water by a spring attached to the bottom of a pail. When the pail is kept in an elevator moving with an acceleration downwards,the spring length

$A$ 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:

$A$ rectangular block is $5 \ cm \times 5 \ cm \times 10 \ cm$ in size. The block is floating in water with the $5 \ cm$ side vertical. If it floats with the $10 \ cm$ side vertical,what change will occur in the level of water?

$A$ metallic block of density $5 \, g \, cm^{-3}$ and having dimensions $5 \, cm \times 5 \, cm \times 5 \, cm$ is weighed in water. Its apparent weight will be

$A$ wooden cylinder floats vertically in water with half of its length immersed. The density of wood is

$A$ metallic body of material with density of $8000\ kg/m^3$ has a cavity inside. $A$ spring balance shows its mass to be $10.0\ kg$ in air and $7.5\ kg$ when immersed in water. The ratio of the volume of the cavity to the volume of the material of the body must be