Two bodies of different masses ma and mb are dropped from two different heights a and b. The ratio of times taken by the two bodies to drop through these distances is :

Foundation

Physics Foundation

Vertical Motion

Force and Newtons Law of Motion

Question

Two bodies of different masses m_a and m_b are dropped from two different heights a and b. The ratio of times taken by the two bodies to drop through these distances is :

$\frac{m_{a}}{m_{b}} \times \frac{b}{a}$

a² : b²

a : b

$\sqrt{a} : \sqrt{b}$

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by S = ut + $\frac{1}{2}$ gt²

a = 0 + $\frac{1}{2}$ g t_A² , b = $\frac{1}{2}$ g.t_B²

$t_{A} = \sqrt{\frac{2 a}{g}}, t_{B} = \sqrt{\frac{2 b}{g}}$

$\frac{t_{A}}{t_{B}} = \frac{\sqrt{a}}{\sqrt{b}} or \sqrt{a} : \sqrt{b}$