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A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 km s⁻¹, the escape velocity from the surface of the planet would be

1. 1.1 km s⁻¹
2. 11 km s⁻¹
3. 110 km s⁻¹
4. 0.11 km s⁻¹

Correct answer: 110 km s⁻¹

Solution

The escape velocity is determined by the formula v = √(2GM/R), where G is the gravitational constant, M is the mass of the planet, and R is its radius. In this case, since the planet is 10 times more massive and has a radius that is 10 times smaller, the escape velocity increases by a factor of √(10/0.1) = √100 = 10, resulting in an escape velocity of 110 km s⁻¹.

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