$A$ piston of cross-section area $100 \, cm^2$ is used in a hydraulic press to exert a force of $10^7 \, dynes$ on the water. The cross-sectional area of the other piston which supports an object having a mass $2000 \, kg$ is:

In a hydraulic jack as shown,the mass of the car is $W = 800 \, kg$,$A_1 = 10 \, cm^2$,and $A_2 = 10 \, m^2$. The minimum force $F$ required to lift the car is ........... $N$.

The area of cross-section of the wider tube shown in the 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 ........ $cm$.

$A$ tall tank filled with water has an irregular shape as shown. The wall $CD$ makes an angle of $45^{\circ}$ with the horizontal,the wall $AB$ is normal to the base $BC$. The lengths $AB$ and $CD$ are much smaller than the height $h$ of water (figure not to scale). Let $p_1, p_2$ and $p_3$ be the pressures exerted by the water on the wall $AB$,base $BC$ and the wall $CD$ respectively. Density of water is $\rho$ and $g$ is acceleration due to gravity. Then,approximately

$A$ hydraulic automobile lift is designed to lift cars with a maximum mass of $3000 \; kg$. The area of cross-section of the piston carrying the load is $425 \; cm^{2}$. What maximum pressure would the smaller piston have to bear?

Why does the bottom of a bottle filled with liquid break when the cork is hit?