A boy can jump to a height h on ground level. What should be the radius of a sphere of density d such that on jumping on it, he escapes out of the gravitational field of the sphere :
Answer & explanation
Correct answer: option 4
When a boy jumps from a ground level up to height h then its velocity of jumping v = √2gh ... (i)
and for the given condition this will become equal to escape velocity vescape :
= \(\sqrt{\frac{2GM}{R}} \)
= \(\sqrt{\frac{2 G}{R}\frac{4}{3} \pi R^3 d}\) ... (ii)
From (i) and (ii) :
\(\sqrt{2gh} = R \sqrt{\frac{2}{3} \pi G d}\)
\(\Rightarrow R = [\frac{3}{4 \pi} \frac{gh}{dG}]^{1/2}\)