A roughly spherical volume of rock 1.5 km in radius is 30% denser than the surro

Question

A roughly spherical volume of rock 1.5 km in radius is 30% denser than the surrounding rock, whose density is 2900 kg/m3. The denser rock is centered 2.1 km below Earth's surface. By what percentage is the surface value of g directly above the denser rock increased due to its excess density? Hint: Treat the "extra" mass of the denser rock as a gravitating sphere, and calculate the gravitational acceleration it produces at Earth's surface.

Please give the answer and detail how to get to that answer clearly.

Explanation / Answer

The extra mass of the denser rock (above the surrounding rock) is ?m= (4/3)piR^33 , where R = 1.3 km is the radius of the spherical volume and ? ?= 30%

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