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 ?
 
Option: 1 1.00\; ms^{-1}
Option: 2 14.41\; ms^{-1}
Option: 3 19.0\; ms^{-1}  
Option: 4 4.47\; ms^{-1}

Answers (1)

Given, \mathrm{m}=0.5 \mathrm{~kg} \ \ and \ \ \mathrm{u}=20 \mathrm{~m} / \mathrm{s}
Initial kinetic energy

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

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