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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 separations between points $A$ and $B$ and between $B$ and $C$ i..e $\frac{A B}{B C}$ is -
Option: 1
1

Option: 2
2

Option: 3
$\frac{10}{7}$

Option: 4
$\frac{20}{7}$

Answers (1)

best_answer

$A \rightarrow \frac{u^2}{4}-u^2=-2 g h_1 \\$
$B \rightarrow \frac{u^2}{9}-u^2=-2 g h_2 \\$
$C \rightarrow \frac{u^2}{16}-u^2=-2 g h_3 \\$
${\therefore A B} =\frac{u^2}{2 g}\left\{\frac{8}{9}-\frac{3}{4}\right\}$
$=\frac{u^2}{2 g} \cdot \frac{5}{36}$ ...................(1)
${B C =\frac{u^2}{2 g}\left\{\frac{15}{16}-\frac{8}{9}\right\} }$
$=\frac{u^2}{2 g} \cdot \frac{7}{144}$ ...................(2)
$\frac{A B}{B C} =\frac{5}{36} \times \frac{144}{7}$

$=\frac{20}{7}$

Posted by

shivangi.shekhar

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