A planet of radius `R=(1)/(10)xx(radius of Earth)` has the same mass density as Earth. Scientists dig a well of depth`(R )/(5)` on it and lower a wire of the same length and a linear mass density `10^(-3) kg m(_1)` into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it inplace is (take the radius of Earth`=6xx10^6m` and the acceleration due to gravity on Earth is `10ms^(-2)`

Options

A. 96 N
B. 108 N
C. 120 N
D. 150 N

Answer

B

Explanation

`g=(GM)/(R^(2))=(4G)/(3)(rhoR^(3))/(R^(2))=(4)/(3)GrhoR`
`g'_(rho)=(g)/(10)=1`
`F = int lambda dyg`
`10^(-3)xxint(GM)/(R^(2))xx(y)/(R )dy`
`=10^(-3)xx1(y^(2))/(2R)|_(R//5)^(R )=(10^(-3))/(2R) [R^(2)-(16R^(2))/(25)]`

`=(9)/(25)xx(R )/(2)xx10^(-3)`
`(9)/(25)xx3xx10^(5)xx10^(-3)=108N`