If ' \(a\) ' represents the velocity ratio of an inclined plane of length \(10 m\) and height \(5 m\) and ' \(b\) ' represents the velocity ratio of a block - and - tackle system consisting of 6 pulleys, \(\frac{(b-a)}{b}\) equals
A. \(1 / 6\) B. \(2 / 3\) C. 2 D. \(1 / 2\)
Correct Answer: B
Explanation
$$ \begin{aligned} \text { V.R. of an inclined plane } &=\frac{\text { Length of plane }}{\text { Height of plane }}=\frac{1}{\sin \theta} \\ &=\frac{10 m }{5 m }=2 \Rightarrow a \end{aligned} $$ V.R. of a pulley system \(=\) number of pulleys \(=6 \Rightarrow b\) Thus, $$ \frac{b-a}{b}=\frac{6-2}{6}=\frac{4}{6}=\frac{2}{3} $$
