If a rubber ball falls from a height h and rebounds up to the height of h/2. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are

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Solution

Q.
If a rubber ball falls from a height $h$ and rebounds up to the height of $h / 2$ . The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are [2024]

1 $40 %, \sqrt{2 g h}$

2 $50 %, \sqrt{\frac{g h}{2}}$

3 $50 %, \sqrt{2 g h}$

4 $50 %, \sqrt{g h}$

Ans.
(3)

Velocity just before collision = $\sqrt{2 g h}$

  Velocity just after collision = $\sqrt{2 g (\frac{h}{2})}$

   $∴$ $∆ K E = \frac{1}{2} m (2 g h) - \frac{1}{2} m g h = \frac{1}{2} m g h$

   $∴$ % loss in energy $\frac{∆ K E}{K E_{i}} \times 100$

$\Rightarrow \frac{∆ K E}{K E_{i}} \times 100 = \frac{\frac{1}{2} m g h}{\frac{1}{2} m g 2 h} \times 100 = 50 %$

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