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One model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M = 6.24 × 10^24 kg and R = 4.11 × 10^6 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet?
One model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M = 6.24 × 10^24 kg and R = 4.11 × 10^6 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet?
(a)At a distance r=R from the centre of the planet, there is no effect due to the outer shell: so, the gravitational field strength at r=R is only determined by the gravity produced by the core of the planet.So, the strength of the gravitational field is given bywhereG is the gravitational constantM = 6.24 × 10^24 kg is the mass of the core of the planetR = 4.11 × 10^6 m is the radius of the coreSubstituting into the equation, we find(b)at distance r=3R from the centre, the particle feels the effect of gravity due to both the core of the planet and the outer shell between R and 2R.So, we have to consider the total mass that exerts the gravitational attraction at r=3R, which is the sum of the mass of the core (M) and the mass of the shell (4M):M' = M + 4M = 5MTherefore, the gravitational acceleration at r=3R will beAnd susbstitutingg = 24.6 m/s^2found in the previous part, we find...