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• Part A The electric field was defined as E = Fon q/q, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the gravitational field g of a point mass? Write your answer using the unit vector î , but be careful with signs; the gravitational force between two "like masses" is attractive, not repulsive. Express your answer in terms of the variables M, r, unit vector î , and the gravitational constant G. Use the 'unit vector' button to denote unit vectors in your answer. • View Available Hint(s) ? =

• Part A The electric field was defined as E = Fon q/q, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the gravitational field g of a point mass? Write your answer using the unit vector î , but be careful with signs; the gravitational force between two "like masses" is attractive, not repulsive. Express your answer in terms of the variables M, r, unit vector î , and the gravitational constant G. Use the 'unit vector' button to denote unit vectors in your answer. • View Available Hint(s) ? =

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I Review Newton's law of gravity and Coulomb's law are both inverse-square laws. Consequently, there should be a "Gauss's law for gravity." Part A The electric field was defined as E = Fon g/g, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the gravitational field g of a point mass? Write your answer using the unit vector r, but be careful with signs; the gravitational force between two "like masses" is attractive, not repulsive. Express your answer in terms of the variables M, r, unit vector î, and the gravitational constant G. Use the 'unit vector' button to denote unit vectors in your answer. • View Available Hint(s)
Transcribed Image Text:I Review Newton's law of gravity and Coulomb's law are both inverse-square laws. Consequently, there should be a "Gauss's law for gravity." Part A The electric field was defined as E = Fon g/g, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the gravitational field g of a point mass? Write your answer using the unit vector r, but be careful with signs; the gravitational force between two "like masses" is attractive, not repulsive. Express your answer in terms of the variables M, r, unit vector î, and the gravitational constant G. Use the 'unit vector' button to denote unit vectors in your answer. • View Available Hint(s)
Part B A spherical planet is discovered with mass M, radius R, and a mass density that varies with radius as p= po (1 – r/2R) , where po is the density at the center. Determine po in terms of M and R. Hint: Divide the planet into infinitesimal shells of thickness dr, then sum (i.e., integrate) their masses. Express your answer in terms of the variables M and R. • View Available Hint(s) ΑΣφ ? Po = Submit Previous Answers Part C Gauss's law for gravity: f ğ · dà = -4mGMm - Find an expression for the gravitational field strength inside the planet at distance r < R. Express your answer in terms of the variables M, r, R, and the gravitational constant G. • View Available Hint(s) ΑΣφ ?
Transcribed Image Text:Part B A spherical planet is discovered with mass M, radius R, and a mass density that varies with radius as p= po (1 – r/2R) , where po is the density at the center. Determine po in terms of M and R. Hint: Divide the planet into infinitesimal shells of thickness dr, then sum (i.e., integrate) their masses. Express your answer in terms of the variables M and R. • View Available Hint(s) ΑΣφ ? Po = Submit Previous Answers Part C Gauss's law for gravity: f ğ · dà = -4mGMm - Find an expression for the gravitational field strength inside the planet at distance r < R. Express your answer in terms of the variables M, r, R, and the gravitational constant G. • View Available Hint(s) ΑΣφ ?
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