University Physics Al No. 4 The gravitational force and the gravitational field Class Number ame I. Choose the Correct Answer 1. The magnitude of the force of gravity between two identical objects is given by Fo. If the mass of each object is doubled but the distance between them is halved, then the new force of between the objects will be (A) A)16F0 (B)4F0 (C)F0 (D)Fo/ Solution GMm The magnitude of the gravitational force is F according to the problem, we get 16—,=16F (r/2)2 2. A spherical symmetric nonrotating body has a density that varies appreciably with the radial distance from the center. At the center of the body the acceleration of free fall A)Definitely larger than zero. (B) Possibly larger than zero (C) Definitely equal to zero Solution At the center, the force acted on the body is zero, so the acceleration of the body is zero 3. The acceleration due to gravity in a hole dug into a nonuniform spherically symmetric body (A)will increase as you go deeper, reaching a maximum at the center (B)will increase as you go deeper, but eventually reach a maximum, and then decrease until you (C)can increase or decrease as you go deeper Solution For a nonuniform spherically symmetric body, the force of gravity depends on the distance from the center which is related to how the density of the body changed with respect to the distance from the center, for instance: according to the Gauss's law of gravity g·ds=4G∑M1=4ad whenp=A/r2, the acceleration g will increase as you go deeper, when p=Ar theUniversity Physics AI No. 4 The Gravitational Force and the Gravitational Field Class Number Name I．Choose the Correct Answer 1. The magnitude of the force of gravity between two identical objects is given by F0. If the mass of each object is doubled but the distance between them is halved, then the new force of gravity between the objects will be （ A ） (A) 16 F0 (B) 4 F0 (C) F0 (D) F0/2 Solution: The magnitude of the gravitational force is 2 r GMm Fgrav = , according to the problem, we get 2 0 2 2 2 16 16 ( / 2) 4 F r Gm r Gm Fgrav ′ = = = 2. A spherical symmetric nonrotating body has a density that varies appreciably with the radial distance from the center. At the center of the body the acceleration of free fall is ( C ) (A) Definitely larger than zero. (B) Possibly larger than zero. (C) Definitely equal to zero. Solution: At the center, the force acted on the body is zero, so the acceleration of the body is zero. 3. The acceleration due to gravity in a hole dug into a nonuniform spherically symmetric body ( C ) (A) will increase as you go deeper, reaching a maximum at the center. (B) will increase as you go deeper, but eventually reach a maximum, and then decrease until you reach the center. (C) can increase or decrease as you go deeper. (D) must decrease as you go deeper. Solution: For a nonuniform spherically symmetric body, the force of gravity depends on the distance from the center which is related to how the density of the body changed with respect to the distance from the center, for instance: according to the Gauss’s law of gravity ∫ ∑ ∫ g ⋅ s = G Mi = G V s d 4π 4π ρd r r when 2 ρ = A r , the acceleration g r will increase as you go deeper, when ρ = Ar the acceleration g r will decrease as you go deeper