A planet of radius R = × (radius of Earth) has the same mass density as Earth. Scientists dig a

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A planet of radius R = &#215; (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 &#215; 106 m and the acceleration due to gravity on Earth is 10 ms-2)

Accepted Answer

RP = = 6 &#215; 105 m &#961;P = &#961;E g = &#960;R3&#961; &#8658; g = &#960;G&#961;R &#8756; &#8658; 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 = (&#955;dx)gx dF = &#955;gdx &#8756; F = gdx = &#955; g = &#955; g = 10-3 &#215; g = 10 -3 &#215; &#215; 6 &#215; 105 &#215; 1 = = 108 N

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