Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. A small hole is made in the side of each tank at the same depth $h$ below the liquid surface, but the hole in tank 1 has half the cross-sectional area of the hole in tank 2. What is the ratio $R_{V 1} / R_{V 2}$ of the volume flow rates from the two tanks?

Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. A small hole is made in the side of each tank at the same depth h below the liquid surface, but the hole in tank 1 has half the cross-sectional area of the hole in tank 2. At one instant, the liquid in tank 1 is $12.0\text{~ cm}$ above the hole. If the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?

The Sun, which is

$$2.2 × 10^20 m$$

from the center of the Milky Way galaxy, revolves around that center once every

$$2.5 × 10^8$$

years. Assuming each star in the Galaxy has a mass equal to the Sun’s mass of

$$2.0 × 10^30 kg$$

, the stars are distributed uniformly in a sphere about the galactic center, and the Sun is at the edge of that sphere, estimate the number of stars in the Galaxy.

Two concentric spherical shells with uniformly distributed masses M1 and M2 are situated as shown in figure. Find the magnitude of the net gravitational force on a particle of mass $m$, due to the shells, when the particle is located at radial distance $a$.

Two concentric uniform thin spherical shells have masses $M_1$ and $M_2$ and radii a and 2a. What is the magnitude of the gravitational force on a point particle of mass m (not shown) located a distance 0.9 a from the center of the shells?

Two concentric uniform thin spherical shells have masses $M_1$ and $M_2$ and radii a and 2a. What is the magnitude of the gravitational force on a point particle of mass m (not shown) located a distance 1.9 a from the center of the shells?

Two concentric uniform thin spherical shells have masses $M_1$ and $M_2$ and radii a and 2a. What is the magnitude of the gravitational force on a point particle of mass m (not shown) located a distance 3a from the center of the shells?

Two concentric spherical shells with uniformly distributed masses M underscore 1 and M underscore 2 are situated as shown in the given figure. Find the magnitude of the net gravitational force on a particle of mass m, due to the shells, when the particle is located at radial distance at c.

Two concentric spherical shells with uniformly distributed masses M underscore 1 and M underscore 2 are situated as shown in the given figure. Find the magnitude of the net gravitational force on a particle of mass m, due to the shells, when the particle is located at radial distance at b.

In the given figure two point particles are fixed on an x axis separated by distance d. Particle A has mass mA and particle B has mass 3.00 mA. A third particle C, of mass 75.0 mA, is to be placed on the x axis and near particles $A$ and $B$. In terms of distance $d$, at what $x$ coordinate should $C$ be placed so that the net gravitational force on particle $A$ from particles $B$ and $C$ is zero?

What must the separation be between a 5.2 kg particle and a 2.4 kg particle for their gravitational attraction to have a magnitude of

$$2.3 × 10^-12 N$$

?

A garden hose with an internal diameter of 1.9 cm is connected to a (stationary) lawn sprinkler that consists merely of a container with 20 holes, each 0.15 cm in diameter. If the water in the hose has a speed of 0.91 m/s, at what speed does it leave the sprinkler holes?

Fresh water flows horizontally from pipe section 1 of cross-sectional area $A_1$ into pipe section 2 of cross-sectional area $A_2$. The figure mentioned gives a plot of the pressure difference $p_2-p_1$ versus the inverse area squared $A_1^{-2}$ that would be expected for a volume flow rate of a certain value if the water flow were laminar. under all circumstances. The scale on the vertical axis is set by $\Delta p_5=$ $450 \mathrm{kN} / \mathrm{m}^2$. For the conditions of the figure, what are the values of (b) the volume flow rate?

Suppose that two tank s, 1 and 2, each with a large opening at the top, contain different liquids. A small hole is made in the side of each tank at the same depth h below the liquid surface, but the hole in tank 1 has half the cross-sectional area of the hole in tank 2. (a) What is the ratio

$$\rho _ { 1 } / \rho _ { 2 }$$

of the densities of the liquid s if the mass flow rate is the same for the two holes? (b) What is the ratio

$$R _ { V 1 } / R _ { V 2 }$$

of the volume flow rates from the two tanks? (c) At one instant, the liquid in tank 1 is 16.0 cm above the hole. If the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?