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)
× (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 mρP = ρE
g =
πR3ρ ⇒ g =
πGρR∴
⇒ gP =
= 1m/s2 Acceleration due to gravity at a depth x
gx =
gPForce on a small segment of wire at a depth x from surface
dF = (λdx)gx
dF = λ
gdx∴ F =
gdx = λ
g= λ
g = 10-3
× g = 10 -3 ×
× 6 × 105 × 1=
= 108 NCreate a free account to view solution
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