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

Options

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

Answer

B

Explanation

`E_(G)=(4piGrrho)/(3)`
`dF=E_(G)lamdadr`
`F=underset((4R)/(5))overset(R)int(4piGrholamda)/(3)rdr=(4piGrholamda)/(3)[(r^(2))/(2)]_((4R)/(5))^(R)`
`=(4piGrholamda)/(3xx2)[R^(2)-(16R^(2))/(25)]=(4pi)/(6)Grholamdaxx(9)/(25)R^(2)`
`F=(4pi)/(6)Gxx(M)/((4pi)/(3)R_(e)^(3))xxlamdaxx(9)/(25)xx(R_(e)^(2))/(100)`
After solving [`Fimplies108N]`