Consider a uniform annular sphere of density $ρ$ and radius $2 m$ and external radius $4 m$ . The gravitational field strength at a point at a distance $r = 3 m$ , from the centre of the sphere is

- \frac{32 G π ρ}{9}

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- 4 G π

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- \frac{32}{27} G π ρ

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- \frac{76}{27} G π ρ

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Solution

The correct option is D $- \frac{76}{27} G π ρ$
$E = - \frac{G M}{r^{2}}$
$E_{g} = - \frac{G M}{9}$
Where $M = ρ \times [\frac{4 π}{3} (3^{3} - 2^{3})]$
Thus $M = \frac{ρ \times 4 π \times 19}{3}$
Hence $E_{g} = - \frac{76 G π ρ}{27}$

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Consider a uniform annular sphere of density ρ and radius 2 m and external radius 4 m. The gravitational field strength at a point at a distance r=3 m, from the centre of the sphere is

The correct option is D −7627GπρE=−GMr2 Eg=−GM9 Where M=ρ×[4π3(33−23)] Thus M=ρ×4π×193 Hence Eg=−76Gπρ27

Consider a uniform annular sphere of density $ρ$ and radius $2 m$ and external radius $4 m$ . The gravitational field strength at a point at a distance $r = 3 m$ , from the centre of the sphere is

The correct option is D $- \frac{76}{27} G π ρ$
$E = - \frac{G M}{r^{2}}$
$E_{g} = - \frac{G M}{9}$
Where $M = ρ \times [\frac{4 π}{3} (3^{3} - 2^{3})]$
Thus $M = \frac{ρ \times 4 π \times 19}{3}$
Hence $E_{g} = - \frac{76 G π ρ}{27}$