Let E₁ and E₂ denote the gravitational field magnitudes at radial distances r₁ and r₂ from the axis of an infinitely long uniform solid cylinder of radius R. Which statement(s) as printed must hold true?
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Question

Let E₁ and E₂ denote the gravitational field magnitudes at radial distances r₁ and r₂ from the axis of an infinitely long uniform solid cylinder of radius R. Which statement(s) as printed must hold true?

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G1 Physics · Accepted Answer

Step 1: For a uniform infinite solid cylinder, g(r)=2πGρr for rR. Therefore if r₁E₂, so B is true. Step 2: For r₁=R-ε and r₂=R+ε, E₁/E₂=[(R-ε)(R+ε)]/R²=1-ε²/R²<1, so E₁