The magnitude of gravitational field at distance r 1 and r 2 from the centre of a uniform sphere of radius R and mass M are E 1 and E 2 respectively. If r 1 R and r 2

Question

The magnitude of gravitational field at distance r 1 ​ and r 2 ​ from the centre of a uniform sphere of radius R and mass M are E 1 ​ and E 2 ​ respectively. If r 1 ​ > R and r 2 ​ < R , then the ratio E 1 ​ / E 2 ​ is

TestHub · Accepted Answer

The magnitude of the gravitational field outside a uniform sphere at a distance $r_{1} > R$ is given by

$E_{1} = \frac{GM}{r _{1}^{2}}$

The magnitude of the gravitational field inside a uniform sphere at a distance $r_{2} < R$ is given by

$E_{2} = \frac{GM r _{2}}{R ^{3}}$

Taking the ratio of $E_{1}$ and $E_{2}$ , we get

$\frac{E _{1}}{E _{2}} = \frac{\frac{GM}{r _{1}^{2}}}{\frac{GM r _{2}}{R ^{3}}} = \frac{R ^{3}}{r _{1}^{2} r _{2}}$

Answer: $\frac{R ^{3}}{r _{1}^{2} r _{2}}$

Physics - Gravitation Question with Solution | TestHub

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