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

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$\frac{10}{7}$

$\frac{20}{7}$

answer is B.

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Detailed Solution

Here, $A = \frac{u^{2}}{4} - u^{2} = - 2 g h_{1}$

$B = \frac{u^{2}}{9} - u^{2} = - 2 g h_{2}$

$a n d C = \frac{u^{2}}{16} - u^{2} = - 2 g h_{3}$

$∴ A B = \frac{u^{2}}{2 g} {\frac{8}{9} - \frac{3}{4}} = \frac{u^{2}}{2 g} . \frac{5}{36}$

$B C = \frac{u^{2}}{2 g} {\frac{15}{16} - \frac{8}{9}} = \frac{u^{2}}{2 g} . \frac{7}{144}$

$∴ \frac{A B}{B C} = \frac{5}{36} \times \frac{144}{7} = \frac{20}{7}$

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