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

(b) `R_P = (R_e)/(10) = 6xx10^5 m`
The mass of the wire ` =10^3
xx 1.2 xx10^5 = 120kg`
Let `g_(PM)` be the acceleration
due to gravity at point M which is the mid point of the
wire and is at depth of `(R_p)/(10)`
Let `g_p` be the acceleration due to gravity at the surface
of th planet.
`g_p = (4)/(3)pirhoGR_P , g_e = (4)/(3) pirhoGR_E`
`:. (gp)/(ge) = (R_p)/(R_e_) = (1)/(100)`
`:. g_p = (10)/(10) =1ms^(-2)`
and `g_(PM) = g_p[1-(R_p//10)/(R_p)] =1[1 -0.1] = 0.9 ms^(-2)`
`:. Force = mass of wire `xxg_(pM) = 120xx0.9 = 108 N`