First slide

Release from certain height

Question

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

Moderate

A

$g_{a}$ : $g_{b}$
B

2 $g_{a}$ : $g_{b}$
C

$g_{a}$ : 2 $g_{b}$
D

√( $g_{a}$ :√( $g_{b}$ )

Solution

$\large {T_A} = {T_B} \Rightarrow \sqrt {\frac{{2{h_A}}}{{{g_A}}}} = \sqrt {\frac{{2{h_B}}}{{{g_B}}}}$
$\large \frac{{{h_A}}}{{{g_A}}} = \frac{{{h_B}}}{{{g_B}}} \Rightarrow \frac{{{h_A}}}{{{h_B}}} = {g_A}/{g_B}$

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