Two bodies whose masses are in the ratio 2:1 are dropped simultaneously at two places A and B where the accelerations due to gravity are g_A and g_B respectively. If they reach the ground simultaneously, the ratio of the heights from which they are dropped is

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$2 g_{A} : g_{B}$

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

$g_{A} : 2 g_{B}$

$g_{A} : g_{B}$

answer is A.

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Detailed Solution

$\begin{array}{l} T_{A} = T_{B} \Rightarrow \sqrt{\frac{2 h_{A}}{g_{A}}} = \sqrt{\frac{2 h_{B}}{g_{B}}} \\ \frac{h_{A}}{g_{A}} = \frac{h_{B}}{g_{B}} \Rightarrow \frac{h_{A}}{h_{B}} = g_{A} / g_{B} \end{array}$

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