A mass of 6 × 10 24 kg is to be compressed in a sphere in such a way that the escape velocity from the sphere is 3 × 10 8 . What should be the radius of the sphere?

Question

A mass of 6 × 10 24 kg is to be compressed in a sphere in such a way that the escape velocity from the sphere is 3 × 10 8 . What should be the radius of the sphere?, 9 km, 9 m, 9 mc, 9 mm

MARKS App · Accepted Answer

Let escape velocity be v e , then kinetic energy is = 1 2 m v e 2 … . i a n d e s c a p e e n e r g y = + G M e m R e … i i Equating Eqs. (i) and (ii), we get 1 2 m e v ⁡ e ⁡ 2 = G ⁡ M ⁡ e ⁡ m ⁡ R ⁡ e ⁡ ⟹ v e = 2 G M e R e ⟹ R = 2 G M e v e 2 Given, G ⁡ = 6.67 × 1 0 - 1 1 N m 2 kg -2 R = 2 × 6.67 × 10 - 11 × 6 × 10 24 ( 3 × 10 8 ) 2 R = 8.89 × 10 - 3 R ≈ 9 × 10 - 3 m = 9 m m

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