question_answer

A hollow wooden cylinder of height A, inner radius R and outer radius 2R is placed in a cylindrical container of radius 3R. When water is poured into the container, the minimum height H of the container for which cylinder can float inside freely is           

A) \[\frac{h{{p}_{water}}}{{{\rho }_{water}}+{{\rho }_{wood}}}\]

B) \[\frac{h{{\rho }_{wood}}}{{{\rho }_{water}}}\]

C) h

D) \[\frac{{{h}^{2}}}{R}\]

Correct Answer: B

Solution :

[b] \[mg=v{{\rho }_{wood}}g=(3\pi {{R}^{2}}h){{\rho }_{wood}}g\] \[\frac{h{{\rho }_{wood}}}{{{\rho }_{water}}}=H\]