# 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.

Question
34 views
 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.
check_circle

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: help_outlineImage TranscriptioncloseMe 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 fullscreen
Step 3

Given tha... help_outlineImage Transcriptionclose(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 fullscreen

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

### Gravitation 