Question

A steel ball is bouncing up and down on a steel plate with a period of oscillation 1 second. If $g=10m{s}^{-2}$, then it bounces up to a height of

• A. $5$ $m$
• B. $10$ $m$
• C. $2.5$ $m$
• D. $1.25$ $m$

Answer 1

The correct option is D $1.25$ $m$

The ball takes 1 second to bounce up and down through the same height; so, the time of fall is equal to time of rise i.e. $\frac{1}{2}$ second.

Using second law of motion, $s=ut+\frac{1}{2}a{t}^2$

Height, $s=h,$ initial velocity, $u=0$
$h=0+\frac{1}{2}g{\left(\frac{1}{2}\right)}^2$
$h=\frac{10}{8}$
$h=1.25m$

So, the ball bounces up to a height of $1.25m$.