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A spherical cavity is made inside a sphe...

A spherical cavity is made inside a sphere of density, `d`. Its centre lies at a distance `l`, from the centre of sphere, show that the gravitational strength, `I`, of the field inside the cavity is `= (4//3) xx pi Gld`.

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The gravitational intensity inside the cavity at a point is due to mass of that spherical portion of the earth on the surface of which the cavity lies.

Let the centre `C` of the cavity be lying on the surface of a solid sphere of radius `OC = l` and density of earth = `d` Fig. `(APC).2`.
Gravitational intensity inside the cavity (i.e., at point `C`) is
`I = (GM')/(l^(2)) = (G)/(l^(2)) xx (4)/(3) pi l^(3) d = (4)/(3)pi G ld`
`= (4)/(3) xx (22)/(7) xx (6.67 xx 10^(-11)) xx (5.5 xx 10^(3))`
`= 1.53 xx 10^(-6) N kg^(-1)`
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