Question

On a given rough inclined plane, a solid sphere and a hollow cylinder are rolled one by one, with same speed. Ratio of heights attained by solid sphere and hollow cylinder is

(1) \(\frac{9}{10}\) 

(2) \(\frac{3}{10}\) 

(3) \(\frac{7}{10}\) 

(4) \(\frac{6}{10}\) 

Answer 1

Correct Option is (3) \(\frac{7}{10}\) 

Conserving energy : 

\(\frac{1}{2}mv^2+\frac{1}{2}lw^2= mgh\) 

\(\Rightarrow\) \(\frac{7}{10}mv^2=mgh_1\) 

& \(m'v^2=m'gh_2\) 

\(\Rightarrow\) \(\frac{7}{10}=\frac{h_1}{h_2}\)