Motion In A Straight Line Ques 37
37. 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
[2006]
(a) $12 / 5$
(b) $5 / 12$
(c) $4 / 5$
(d) $5 / 4$
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Answer:
Correct Answer: 37.(c)
Solution:
- (c) Let $t_1$ & $t_2$ be the time taken by $A$ and $B$ respectively to reach the ground then from the formula,
$h=\frac{1}{2} g t^{2}$,
For first body, $ 16=\frac{1}{2} g t_1{ }^{2}$
For second body, $25=\frac{1}{2} g t_2{ }^{2}$
$\therefore \frac{16}{25}=\frac{t_1^{2}}{t_2^{2}} \Rightarrow \frac{t_1}{t_2}=\frac{4}{5}$.
If a body is a dropped from some height, the motion is independent of mass of the body. The time taken to reach the ground $t=\sqrt{2 h / g}$ and final velocity $V=\sqrt{2 g h}$ and initial velocity, $u=0$.
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