Question

A rubber ball is dropped from a height of $5m$ on a planet where the acceleration due to gravity is same as that on the surface of the earth. On bouncing, it rises to a height of $1.8m$. the ball loses its velocity by a factor of

• A. $\frac{3}{5}$
• B. $\frac{9}{25}$
• C. $\frac{2}{5}$
• D. $\frac{16}{25}$

Answer 1

The correct option is C $\frac{2}{5}$

Given,

Height from which ball is dropped $s=5m$

Height attend by ball after bouncing $s^{\prime }=1.8m$

Gravitational acceleration $g=9.8m/s^2$

We know by third equation of kinetic motion,
$v^2-u^2=2gs$
where $v=$ final velocity , $u=$ initial velocity ,$S=$ distance
Now, for downward motion, $u=0$
$v^2-0=2\times 9.8\times 5$
$\Rightarrow v=\sqrt{98}=9.9$

Also for upward motion, $v=0$
$0^2-u^2=2\times (-9.8)\times 1.8$
$\Rightarrow u=\sqrt{3528}=5.94$

Fractional loss $=\frac{9.9-5.94}{9.9}=0.4$ or $\frac{2}{5}$

Option C