Motion in a Straight Line - Result Question 40

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41. 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

======= ####41. 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

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/motion-in-a-straight-line/motion-in-a-straight-line—result-question-40.md (a) $12 / 5$

(b) $5 / 12$

(c) $4 / 5$

(d) $5 / 4$

[2006]

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Answer:

Correct Answer: 41. (c)

Solution:

  1. (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, $\quad 16=\frac{1}{2} g t_1{ }^{2}$

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, $u=0$. (a) For part $A B$

From 3rd equation of motion $v^{2}=u^{2}-2 gH$

$0=u^{2}-2 g(H / 2)=u^{2}-gH$

$H=\frac{u^{2}}{g}=\frac{10^{2}}{10}=10 m$