Question #484de

1 Answer
Feb 18, 2017

Answer:

#93.2N#.

If we rely on the posted correct answer, depth should be #3200km#

Explanation:

Calculate gravitational force between body and mass of part sphere of earth which lies below 320 km. Force due to outer spherical shell tends to cancel out.

Mass of earth #M=4/3piR^3rho#
where #R# is radius of earth #rho# is density of earth.
mass of earth sphere below #320km# below earth's surface
#M_d=4/3pi(R-3.2xx10^5)^3 rho# .....(1)
Acceleration due to gravity at the location of body#g_d=GM_s/(R-3.2xx10^5)^2#
Inserting value from (1) we get
#g_d=G(4/3pi(R-3.2xx10^5)^3 rho)/(R-3.2xx10^5)^2#
#=>g_d=4/3Gpirho(R-3.2xx10^5) # ......(2)
We know that acceleration due to gravity at the surface in terms of equation (2)
#g=9.81ms^-2=4/3GpirhoR# .....(3)

Dividing (2) by (3) we get
#g_d/9.81=(4/3Gpirho(R-3.2xx10^5))/(4/3GpirhoR) #
#=>g_d=9.81((R-3.2xx10^5))/R #

Taking average radius of earth as #6400km#, we get
#g_d=9.81((6.4xx10^6-3.2xx10^5))/(6.4xx10^6) #
#g_d=9.32ms^-1#
Weight of #10kg# body #=10xx9.32=93.2N#