Question

A stone falls freely under gravity. It covers distances $h_1,h_2$ and $h_3$ in the first $5second$, the next $5s$ and next $5second$ respectively. The relation between $h_1,h_2$ and $h_3$ is :

• A. $h_1={2h}_2=3h_3$
• B. $h_1=\frac{h_2}{3}=\frac{h_3}{5}$
• C. $h_2=3h_{1}and{h}_3=3h_2$
• D. $h_1=h_2=h_3$

Answer 1

The correct option is B $h_1=\frac{h_2}{3}=\frac{h_3}{5}$

Given, $u=0$

We will use equation of motion:

$s=ut+\frac{1}{2}g{t}^2$
and, $v=u+at$

In the first $5sec$, height covered will be:
$h_1=0+\frac{1}{2}g(5{)}^2$
$\Rightarrow h_1=125m$

after first $5sec$, the velocity will be:
$v_1=0+g\left(5\right)=50m/s$

and, in the next five seconds, height covered will be:

$h_2=50\left(5\right)+\frac{1}{2}g(5{)}^2=375m$

and velocity is, $v_2=v1+gt$,

$v_2=50+g\left(5\right)=100m/s$.

so, in next $5sec$, height covered will be:

$h_3=100\left(5\right)+\frac{1}{2}g(5{)}^2=500+125$
$\Rightarrow h_3=625m$

so, $h_1=\frac{h_2}{3}=\frac{h_3}{5}$
So, the correct option is $\left(B\right)$