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A mass of 6 × 1024 kg (equal to the mass of the earth) is to be compressed in a sphere in such a way that the escape velocity from its surface is 3 × 108 m s-1. What should be the radius of the sphere?

A mass of 6 × 1024 kg (equal to the mass of the earth) is to be compressed in a sphere in such a way that the escape velocity from its surface is 3 × 108 m s-1. What should be the radius of the sphere?

Grade:11

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
8 years ago
Sol. The man of the sphere = 6 × 10^24 kg. Escape velocity = 3 × 10^8 m/s V base c = √2GM/R Or R = 2GM/V base c^2 = 2 * 6.67 * 10^-11 * 6 * 10^24/(3 * 10^8)^2 = 80.02/9 × 10^–3 = 8.89× 10^–3 m = 9 mm.

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