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Assume a planet is a uniform sphere of radius R that (somehow) has a narrow radial tunnel through its center. Also assume we can position an apple anywhere along the tunnel or outside the sphere. Let FR be the magnitude of the gravitational force on the apple when it is located at the planet's surface. How far from the surface (what multiple of R) is there a point where the magnitude of the gravitational force on the apple is 0.3 FR if we move the apple (a) away from the planet and (b) into the tunnel?
Assume a planet is a uniform sphere of radius R that (somehow) has a narrow radial tunnel through its center. Also assume we can position an apple anywhere along the tunnel or outside the sphere. Let FR be the magnitude of the gravitational force on the apple when it is located at the planet's surface. How far from the surface (what multiple of R) is there a point where the magnitude of the gravitational force on the apple is 0.3 FR if we move the apple (a) away from the planet and (b) into the tunnel?
The answers to your question are as listed belowA) If we move the apple0.3 FR awayfrom the planet the value of h is ;0.825 RB) If we move the apple0.3 FR intothe tunnel the distance is ;0.7 RAssumptions :mass of apple = mForce on apple at planet surface == GMm / R² --- ( 1 )Determine th value of ha) Applying equation ( 1 )gravitational force of apple at h = 0.3 FRtherefore equation ( 1 ) becomes0.3 FR = GMm / (R + h)² ----- ( 2 )divide both sides of equation by1 / 0.3 = ( R + h )²/ R²therefore :h = 0.825 Rb) When we go into thetunnelApplying the relation below0.3 FR = G *4/3 π *( R - h )³* dm / (R-h)² -- ( 3 )where : d = density of planetresolvingequation ( 3 )FR = G *4/3πR * dmdividing both sides of the equation0.3 = ( R - h ) / Rtherefore :h = 0.7 RHence we can conclude that A) If we move the apple0.3 FR awayfrom the planet the value of h is0.825 Rand If we move the apple0.3 FR intothe tunnel the distance is ;0.7 RLearn more aboutplanet surface:brainly.com/question/23661578...