Motion In A Straight Line Ques 32
32. A stone falls freely under gravity. It covers distances $h_1, h_2$ and $h_3$ in the first $5$ seconds, the next $5$ seconds and the next $5$ seconds respectively. The relation between $h_1, h_2$ and $h_3$ is
[2013]
(a) $h_1=\frac{h_2}{3}=\frac{h_3}{5}$
(b) $h_2=3 h_1$ and $h_3=3 h_2$
(c) $h_1=h_2=h_3$
(d) $h_1=2 h_2=3 h_3$
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Answer:
Correct Answer: 32.(a)
Solution:
- (a) $\because \quad h=\frac{1}{2} g t^{2}$
$\therefore \quad h_1=\frac{1}{2} g(5)^{2}=125$
$h_1+h_2=\frac{1}{2} g(10)^{2}=500$
$\Rightarrow h_2=375$
$ h_1+h_2+h_3=\frac{1}{2} g(15)^{2}=1125 $
$\Rightarrow h_3=625$
$h_2=3 h_1, h_3=5 h_1$
or $\quad h_1=\frac{h_2}{3}=\frac{h_3}{5}$
The distance covered in time $t, 2 t, 3 t$, etc. will be in the ratio of $1^{2}: 2^{2}: 3^{2}$ i.e., square of integers i.e., $h$ $\propto t^{2}$.
BETA
