A man can throw a ball at a speed on the earth which can cross a river of width $$10$$ m. The man reaches on an imaginary planet whose mean density is twice that of the earth. Find out the maximum possible radius of the planet (in$$ $$km) so that if the man throws the ball at the same speed it may escape from the planet. Given radius of the earth $$=$$ $$6.4$$ x $$106$$ m.

Question

A man can throw a ball at a speed on the earth which can cross a river of width $$10$$ m. The man reaches on an imaginary planet whose mean density is twice that of the earth. Find out the maximum possible radius of the planet (in$$ $$km) so that if the man throws the ball at the same speed it may escape from the planet. Given radius of the earth $$=$$ $$6.4$$ x $$106$$ m.

Infinity Learn · Accepted Answer

Let the speed of the ball which can cross $$10$$ m wide river be V. Then $$R=V2sin$$⁡$$2$$×$$45$$∘$$g=10$$,$$v=10gLet$$ the radius of planet be ' Rp', then mass of the $$planetMp=43$$$$π$$$$Rp3$$×$$2$$σ$$=43$$$$π$$$$Rp3$$×$$2$$×$$Me4/3$$$$π$$$$ReR=2MeRp3Re3Escape$$ velocity of the $$PlanetVe=2GMpRp=2G$$×$$2$$×$$MeRp3Rp$$×$$Re3=10GMeRe22Rp=10Re$$⇒$$2Rp=10$$×$$6.4$$×$$106$$⇒ $$Rp=8$$×$$1032=4$$×$$103=4km$$

Motion of planets and satellites

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