Q.

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.

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answer is 4.

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Detailed Solution

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=43πRp3×2σ=43πRp3×2×Me4/3πReR=2MeRp3Re3Escape velocity of the PlanetVe=2GMpRp=2G×2×MeRp3Rp×Re3=10GMeRe22Rp=10Re⇒2Rp=10×6.4×106⇒ Rp=8×1032=4×103=4km
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