Question

A boy is rolling a $0.5\, kg$ ball on the frictionless floor with the speed of $20 \,ms ^{-1}$. 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. $19.0 \,ms ^{-1}$
• B. $4.47\, ms ^{-1}$
• C. $14.41\, ms ^{-1}$
• D. $1.00\, ms ^{-1}$

Answer 1

Answer: (B)

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