A uniform solid sphere of mass m2=180 kg and radius R2=1.21 m is inside and conc
ID: 2092792 • Letter: A
Question
A uniform solid sphere of mass m2=180 kg and radius R2=1.21 m is inside and concentric with a spherical shell of mass m1=288 kg and radius R1=2.5 m. G=6.67259x10^-11.
a) Find the magnitude of the gravitational force exerted by teh sphere and spherical shell on a particle of mass 2 kg located at a distance .72 m from the center of the sphere and spherical shell. Answer inunits of N,
b) Find the magnitude of the gravitational force exerted by teh sphere and spherical shell on a particle of mass 2 kg located at a distance 1.91 m from the center of the sphere and spherical shell. Answer in units of N.
c) Find the magnitude of the gravitational force exerted by the sphere and spherical shell on a particle of mass 2 kg located at a distance 2.77 m from the center of the sphere and spherical shell. Answer in units of N.
Explanation / Answer
a)density of inner mass= 180/(4*pi*1.21^3/3)
mass within 0.72 m = (4*pi*0.72^3/3)*density
= 180*(0.72/1.21)^3 = 37.91 kg
F= G*m1m2/r^2
= G*37.91*2/(0.72^2) = 9.75x10^-9 N
b) m1= 180 ; m2= 2
F=G*180*2/(1.91^2) = 6.58x10^-9 N
c) m1= 180+288=468 kg; m2 = 2kg ; r= 2.77
F=G*468*2/(2.77^2) = 8.13x10^-9 N
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