Question

Question #484de

Answer 1

`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`