Question

Drops of water fall at regular intervals from the roof of a building of height $H=16\text{m}$. The first drop strikes the ground at the same moment when the fifth drop detaches itself from the roof. The distances between the different drops in air as the first drop reaches the ground are

• A. $1\text{m},4\text{m},7\text{m},10\text{m}$
• B. $1\text{m},3\text{m},5\text{m},7\text{m}$
• C. $1\text{m},4\text{m},9\text{m},16\text{m}$
• D. None of the above

Answer 1

The correct option is B $1\text{m},3\text{m},5\text{m},7\text{m}$


Here, $x$ is the time interval of fall of water drops.

We have, $H=16m$
$s=\frac{1}{2}g{t}^2$
$16=\frac{1}{2}10.(4x{)}^2$
$\Rightarrow x=\frac{1}{\sqrt{5}}s$ or $x^2=\frac{1}{5}{s}^2$

Hence the distances of other drops can now be calculated:
At $t=3x$, $h=\frac{1}{2}g(3x{)}^2$
$h=0.5\times 10\times \frac{9}{5}=9m$
Similarly, at $t=2x$, $h=4m$
at $t=x$, $h=1m$


Hence the distances between different drops are $1m,3m,5m,7m.$