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. $\frac{AB}{BC}$ is

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

Answer 1

Answer: (D)

Using the relation, $v^2-u^2=2aS,$ 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 $C,\frac{u^2}{16}-u^2=2(-g)h_3$
$\therefore AB=h_2-h_1=\frac{u^2}{2g}\left[\frac{8}{9}-\frac{3}{4}\right]$
$=\frac{u^2}{2g}\times \frac{5}{36}$
$BC=h_3-h_2=\frac{u^2}{2g}\left[\frac{15}{16}-\frac{8}{9}\right]$
$=\frac{u^2}{2g}\times \frac{7}{144}$
$\therefore \frac{AB}{BC}=\frac{5}{36}\times \frac{144}{7}=\frac{20}{7}$