A ball falls on the ground from a height of 10m and rebounds to a height of 8m. What is the percentage loss kinetic energy of the ball? `(g=10m//s^(2))`

Options

A. 0.2
B. 0.3
C. 0.1
D. 155

Explanation

To find the percentage loss in kinetic energy of the ball, we can follow these steps:

### Step 1: Calculate the initial potential energy (PE_initial) when the ball is at a height of 10m.
The potential energy at a height \( h \) is given by the formula:
\[ PE = mgh \]
where:
- \( m \) is the mass of the ball (which will cancel out),
- \( g \) is the acceleration due to gravity (given as \( 10 \, m/s^2 \)),
- \( h \) is the height (10m in this case).

Thus, the initial potential energy is:
\[ PE_{initial} = mg \cdot 10 \]

### Step 2: Calculate the final potential energy (PE_final) when the ball rebounds to a height of 8m.
Using the same formula for potential energy:
\[ PE_{final} = mg \cdot 8 \]

### Step 3: Calculate the initial kinetic energy (KE_initial) just before hitting the ground.
When the ball falls from a height of 10m, all the potential energy converts to kinetic energy just before it hits the ground. Therefore:
\[ KE_{initial} = PE_{initial} = mg \cdot 10 \]

### Step 4: Calculate the final kinetic energy (KE_final) just after rebounding to a height of 8m.
Similarly, when the ball rebounds to a height of 8m, the potential energy at that height is equal to the kinetic energy just after the rebound:
\[ KE_{final} = PE_{final} = mg \cdot 8 \]

### Step 5: Calculate the loss in kinetic energy.
The loss in kinetic energy can be calculated as:
\[ \text{Loss in KE} = KE_{initial} - KE_{final} \]
Substituting the values we found:
\[ \text{Loss in KE} = (mg \cdot 10) - (mg \cdot 8) = mg \cdot (10 - 8) = mg \cdot 2 \]

### Step 6: Calculate the percentage loss in kinetic energy.
The percentage loss in kinetic energy is given by:
\[ \text{Percentage Loss} = \left( \frac{\text{Loss in KE}}{KE_{initial}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Loss} = \left( \frac{mg \cdot 2}{mg \cdot 10} \right) \times 100 = \left( \frac{2}{10} \right) \times 100 = 20\% \]

### Final Answer:
The percentage loss in kinetic energy of the ball is **20%**.

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