Question

A body is thrown vertically up with a velocity $u$. It passes three points $A, B$ and $C$ in its upward journey with velocities $\frac{u}{2}, \frac{u}{3}$ and $\frac{u}{4}$ respectively. The ratio of the separation between points $A$ and $B$ and between $B$ and $C$ i.e. $\frac{A B}{B C}$ is

• A. 1
• B. 2
• C. $\left(\frac{10}{7}\right)$
• D. $\left(\frac{20}{7}\right)$

Answer 1

Answer: (D)

Using the relation, $v^{2}-u^{2}=2 a S,$ we have
For motion from $O$ to $A, \frac{u^{2}}{4}-u^{2}=2(-g) h_{1}$
For motion from $O$ to $B, \frac{u^{2}}{9}-u^{2}=2(-g) h_{2}$
For motion from $O$ to $C, \frac{u^{2}}{16}-u^{2}=2(-g) h_{3}$
$\therefore A B=h_{2}-h_{1}=\frac{u^{2}}{2 g}\left[\frac{8}{9}-\frac{3}{4}\right]$
$=\frac{u^{2}}{2 g} \times \frac{5}{36}$
$B C=h_{3}-h_{2}=\frac{u^{2}}{2 g}\left[\frac{15}{16}-\frac{8}{9}\right]$
$=\frac{u^{2}}{2 g} \times \frac{7}{144}$
$\therefore \frac{A B}{B C}=\frac{5}{36} \times \frac{144}{7}=\frac{20}{7}$