Question
Asked Oct 22, 2019
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A person weighing 260 lbs on the surface of Earth exerts the same force on a bathroom scale on the surface of Planet X whose mass is 1.9 x Earth's mass. Assume the average density of Earth is 5488 kg/cu.m. determine the density of Planet X in kg/cu.m.
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Expert Answer

Step 1

Given information:

Mass of the person (m) = 260 lbs =  

Mass of planet X (Mx) = 1.9 Me

Where “Me” is mass of planet earth.

Density of the earth given (ρe) = 5288 kg/m3

Let “Rx” be the radius of the planet,

“ρx” be the density of the planet,

“Re” be the radius of earth,

“g” is acceleration due to gravity on earth = 9.81 m/s

Step 2

Given force exerted by the person on the earth and the planet X is same. Prom Newton law of gravity we can write:

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Me g = G Equation (1) mg = GMem But we know that the mass of earth can be written as . Equation (2)where TR23 is the volume (Ve) of planet earth) Me PeTR Substitute equation (1) in equation (2) we get: g= GpeR 6.67 x 10-11 N m2/kg2 Where "G" is universal gravitational constant and G In the above equation we substitute the necessary values, we get: Re 6.4 x 106 m (can be seen in intemet also) Since it is given that the force exerted by the person on both the planet is same, we can write: Meт g G Мx mg = G Hence, we can also deduce that (as shown above) . Equation (3) g= GpxR In the above equation we substitute the necessary values, we get: 35.11 x 109 = PXRX

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Step 3

Given tha...

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(P)nR319(P)R3 - (P)R. Equation (4) 1.9 (P)TR, Mx = 1.9M Divide equation (4) with equation (3) we get: 1.9(5488)(6.4 x 106)3 4 (6.67 x 10-11)n 9.81 We get: Rr = 8.823 x 106 m

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