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Chapter 1: 4 (page 27)
The density of gold is 19.3 g/cm3 . What is this value in kilograms per cubic meter?
The density of gold in kg/m3 is 19300 kg/m3.
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For a spherical planet with mass , volume , and radius ,derive an expression for the acceleration due to gravity at the planet’s surface, , in terms of the average density of the planet, , and the planet’s diameter, . The table gives the values of and for the eight major planets:
(a) Treat the planets as spheres. Your equation for as a function of
and
shows that if the average density of the planets is constant, a graph of
versus
will be well represented by a straight line. Graph
as a function of
for the eight major planets. What does the graph tell you about the variation in average density? (b) Calculate the average density for each major planet. List the planets in order of decreasing density, and give the calculated average density of each. (c) The earth is not a uniform sphere and has greater density near its center. It is reasonable to assume this might be true for the other planets. Discuss the effect this nonuniformity has on your analysis. (d) If Saturn had the same average density as the earth, what would be the value of
at Saturn’s surface?
In 2005 astronomers announced the discovery of large black hole in the galaxy Markarian 766 having clumps of matter orbiting around once every and moving at . (a) How far these clumps from the center of the black hole? (b) What is the mass of this black hole, assuming circular orbits? Express your answer in kilogram and as a multiple of sun’s mass. (c) What is the radius of event horizon?
A closed and elevated vertical cylindrical tank with diameter 2.00 m contains water to a depth of 0.800 m. A worker accidently pokes a circular hole with diameter 0.0200 m in the bottom of the tank. As the water drains from the tank, compressed air above the water in the tank maintains a gauge pressure of 5 X 103Pa at the surface of the water. Ignore any effects of viscosity. (a) Just after the hole is made, what is the speed of the water as it emerges from the hole? What is the ratio of this speed to the efflux speed if the top of the tank is open to the air? (b) How much time does it take for all the water to drain from the tank? What is the ratio of this time to the time it takes for the tank to drain if the top of the tank is open to the air?
A cylindrical bucket, open at the top, is 25.0 cm high and 10.0 cm in diameter. A circular hole with a cross-sectional area 1.50 cm2 is cut in the center of the bottom of the bucket. Water flows into the bucket from a tube above it at the rate of 2.40 x 10-4m3/s. How high will the water in the bucket rise?
A cube of oak wood with very smooth faces normally floats in water. Suppose you submerge it completely and press one face flat against the bottom of a tank so that no water is under that face. Will the block float to the surface? Is there a buoyant force on it? Explain.
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