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Two bodies, A (of mass 1 kg) and B (of mass 3 kg), are dropped from heights of 16 m and 25 m respectively. The ratio of the time taken by them to reach the ground is :-
A
$\dfrac{5}{4}$
B
$\dfrac{12}{5}$
C
$\dfrac{5}{12}$
D
$\dfrac{4}{5}$
Detailed Solution
For a body dropped from rest: $h = \dfrac{1}{2}gt^2 \Rightarrow t = \sqrt{\dfrac{2h}{g}}$
The time of fall does not depend on the mass of the body, so the masses 1 kg and 3 kg play no role.
$\dfrac{t_1}{t_2} = \sqrt{\dfrac{h_1}{h_2}}$
$= \sqrt{\dfrac{16}{25}}$
$= \dfrac{4}{5}$
The time of fall does not depend on the mass of the body, so the masses 1 kg and 3 kg play no role.
$\dfrac{t_1}{t_2} = \sqrt{\dfrac{h_1}{h_2}}$
$= \sqrt{\dfrac{16}{25}}$
$= \dfrac{4}{5}$