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A uniform sphere has a mass M and radius...

A uniform sphere has a mass M and radius R. Find the pressure p inside the sphere, caused by gravitational compression, as a function of the distance r from its centre. Evaluate p at the centre of the Earth, assuming it to be a uniform sphere.

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To find the pressure \( p \) inside a uniform sphere caused by gravitational compression as a function of the distance \( r \) from its center, we can follow these steps: ### Step 1: Define the Density The density \( \rho \) of the uniform sphere can be defined as: \[ \rho = \frac{M}{V} = \frac{M}{\frac{4}{3} \pi R^3} \] where \( M \) is the mass of the sphere and \( R \) is its radius. ...
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Knowledge Check

  • Two spheres each of mass M and radius R are separated by a distance of r . The gravitational potential at the midpoint of the line joining the centres of the spheres is

    A
    `-(GM)/(r )`
    B
    `-(2GM)/( r)`
    C
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    D
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    C
    `(GMm)/(25R^(2)`
    D
    `(GMm)/(100R^(2))`
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