Water flows out of the hole on the side of a bucket and follows a parabolic path. If the bucket falls freely under gravity, ignoring air resistance, the water flow

The area of cross-section of the wider tube shown in figure is $800$ $cm^2$. If a mass of $12$ $ kg $ is placed on the massless piston, the difference in heights $h$ in the level of water in the two tubes is  ........ $cm$

Write and prove Archimedes principle.

A homogeneous solid cylinder of length $L$$(L < H/2)$. Cross-sectional area $A/5$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid as shown in the fig. The lower density liquid is open to atmosphere having pressure ${P_0}$. Then density $D$  of solid is given by

A block of wood floats in water with $\frac{4}{5}$ th of its volume submerged, but it just floats in another liquid. The density of liquid is (in $kg / m ^3$ )

A balloon of mass $m$ contains water of mass $M$ . If it is completely immersed in water, find the apparent mass of the balloon with water in it