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A planet has radius R = (1/10) of Earth's radius and the same mass density as Earth. A well of depth R/5 is dug on the planet, and a uniform wire of length R/5 and linear mass density 10⁻³ kg/m is lowered into it so that it hangs from the top without touching the walls. Find the force a person must apply at the top of the wire to hold it. (Take Earth's radius = 6 * 10⁶ m and g on Earth = 10 m/s².)
- 96 N
- 108 N
- 120 N
- 150 N
Correct answer: 108 N
Solution
With equal density, g at the planet's surface is one-tenth of Earth's. Inside, g(r) = g_surface * r/R_planet. Integrating the wire's weight from the surface down to depth R/5 gives the holding force.
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