Suppose the glass of the previous problem is covered by a jar and the air inside the jar is completely pumped out. (a) What will be the answers to the problem? (b) Show that the answers do not change if a glass of different shape is used provided the height, the bottom area and the volume are unchanged.

The weight of an empty balloon on a spring balance is W₁. The weight becomes W₂ when the balloon is filled with air. Let the weight of the air itself be ω. Neglect the thickness of the balloon when it is filled with air. Also neglect the difference in the densities of air inside and outside the balloon.

A solid float in a liquid in a partially dipped position.

(a) Pressure decreases as one ascends the atmosphere. If the density of air is ρ, what is the change in pressure dp over a differential height dh?

(b) Considering the pressure p to be proportional to the density, find the pressure p at a height h if the pressure on the surface of the earth is p₀.

(c) If p0 = 1.03×10⁵ N m^-2, ρ0 = 1.29 kg m^-3 and g = 9.8 m s^-2, at what height will the pressure drop to (1/10) the value at the surface of the earth?

(d) This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.

An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters 2.5 cm and 3.75 cm. The ratio of the velocities in the two pipes is

Streamline flow is more likely for liquids with

Pressure is a scalar quantity because

A wooden block of mass 0.5 kg and density 800 kg m^-3 is fastened to the free end of a vertical spring of spring constant 50 N m^-1 fixed at the bottom. If the entire system is completely immersed in water find (a) the elongation (for compression) of the spring in equilibrium and (b) the time-period of vertical oscillations of the block when it is slightly depressed and released.

In the derivation of P₁ - P₂ = ρgz, it was assumed that the liquid is incompressible. Why will this equation not be strictly valid for a compressible liquid?

A metal piece of mass 160 g lies in equilibrium inside a glass of water (figure 13-E4). The piece touches the bottom of the glass at a small number of points. If the density of the metal is 8000 kg m4, find the normal force exerted by the bottom of the glass on the metal piece.

Solve the previous problem if the lead piece is fastened on the top surface of the block and the block is to float with its upper surface just dipping into water.