A boy is rolling a 0.5 , kg ball on the frictionless floor with t… - Vidyadip

MCQ

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 ? (in $ms ^{-1}$)

A
$19.0$
✓
$4.47$
C
$14.41$
D
$1.00$

✓

Answer

Correct option: B.

$4.47$

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 :

$k_{ f }=5=\frac{1}{2} mv ^{2}$

$\Rightarrow v ^{2}=20$

$\Rightarrow v =\sqrt{20}=4.47 m / s$

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