A ball is thrown vertically downwards from a height of 20 m with an initial velocity v_0 . It collides with the ground, loses 50 percent of its energy - Physics MCQ Physics | ExamTest.live

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A ball is thrown vertically downwards from a height of 20 m with an initial velocity v_{0} . It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v_{0} is: (Take g = 10 m s^{- 2})

A $10 m s^{- 1}$
B $14 m s^{- 1}$
C $20 m s^{- 1}$
D $28 m s^{- 1}$

Solution & Step-by-step Explanation

1. Energy before collision E_{i} = m g h + \frac{1}{2} m v_{0}^{2} .2. Energy after collision E_{f} = 0.5 E_{i} = 0.5 (m g h + \frac{1}{2} m v_{0}^{2}) .3. The ball rebounds to height h, so E_{f} = m g h . m g h = 0.5 (m g h + \frac{1}{2} m v_{0}^{2}) \Rightarrow 2 m g h = m g h + 0.5 m v_{0}^{2} m g h = 0.5 m v_{0}^{2} \Rightarrow v_{0}^{2} = 2 g h = 2 \times 10 \times 20 = 400 v_{0} = 20 m/s .

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A ball is thrown vertically downwards from a height of 20 m with an initial velocity v_{0} . It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v_{0} is: (Take g = 10 m s^{- 2})

10 m s^{- 1}

14 m s^{- 1}

20 m s^{- 1}

28 m s^{- 1}

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A ball is thrown vertically downwards from a height of $20 m$ with an initial velocity $v_{0}$ . It collides with the ground, loses $50$ percent of its energy in collision and rebounds to the same height. The initial velocity $v_{0}$ is: (Take $g = 10 m s^{- 2}$ )

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A ball is thrown vertically downwards from a height of 20m with an initial velocity v0​. It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v0​ is: (Take g=10m s−2)

Solution & Step-by-step Explanation

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Discussion

A ball is thrown vertically downwards from a height of $20 m$ with an initial velocity $v_{0}$ . It collides with the ground, loses $50$ percent of its energy in collision and rebounds to the same height. The initial velocity $v_{0}$ is: (Take $g = 10 m s^{- 2}$ )