Question

A boy is rolling a $0.5kg$ ball on the frictionless floor with the speed of $20m{s}^{-1}$. The ball gets deflected by an obstacle on the way. After deflection it moves with $5\%$ of its initial kinetic energy. What is the speed of the ball now?

• A. $19.0m{s}^{-1}$
• B. $4.47m{s}^{-1}$
• C. $14.41m{s}^{-1}$
• D. $1.00m{s}^{-1}$

Answer 1

Answer: (B)

Given, $m=0.5kg$ and $u=20m/s$
Initial kinetic energy $\left(k_i\right)=\frac{1}{2}m{u}^2$
$=\frac{1}{2}\times 0.5\times 20\times 20=100J$
After deflection it moves with $5\%$ of $k_i$
$\therefore k_f=\frac{5}{100}\times k_i\Rightarrow \frac{5}{100}\times 100$
$\Rightarrow k_f=5J$
Now, let the final speed be 'v' $m/s$, then :
$k_f=5=\frac{1}{2}m{v}^2$
$\Rightarrow v^2=20$
$\Rightarrow v=\sqrt{20}=4.47m/s$