The diameters of two pistons of a hydraulic press are $0.1\, m$ and $0.6\, m$ respectively. What is the mechanical advantage of the hydraulic press,assuming the effort is applied directly on the pump plunger?

Air is blown through a hole on a closed pipe containing liquid. Then the pressure will

$A$ 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

Given below are two statements:
Statement $I :$ Pressure in a reservoir of water is same at all points at the same level of water.
Statement $II :$ The pressure applied to enclosed water is transmitted in all directions equally.
In the light of the above statements,choose the correct answer from the options given below:

Two syringes of different cross-sections (without needles) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are $1.0 \; cm$ and $3.0 \; cm$ respectively.
$(a)$ Find the force exerted on the larger piston when a force of $10 \; N$ is applied to the smaller piston.
$(b)$ If the smaller piston is pushed in through $6.0 \; cm$,how much does the larger piston move out?

$A$ 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: