JEE Advanced | 2014Basic Maths and Units and DimensionsHard

Question

A planet of radius R = × (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth on it and lower a wire of the same length and of 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 in place is (take the radius of Earth = 6 × 106 m and the acceleration due to gravity on Earth is 10 ms-2)

Options

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

Solution

         
RP = = 6 × 105 m
ρP = ρE
g = πR3ρ
⇒ g = πGρR
⇒ gP = = 1m/s2
Acceleration due to gravity at a depth x
gx = gP
Force on a small segment of wire at a depth x from surface
dF = (λdx)gx
dF = λgdx
∴ F = gdx = λ g
= λ g = 10-3 × g = 10 -3 × × 6 × 105 × 1
= = 108 N

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