A ball dropped from a height of 2 m rebounds to a height of 1.5 m after hitting the ground. Then the percentage of energy lost is

Options

A. 25
B. 30
C. 50
D. 100

Explanation

To find the percentage of energy lost when a ball is dropped from a height of 2 meters and rebounds to a height of 1.5 meters, we can follow these steps:

### Step 1: Calculate the initial potential energy (PE_initial)
The potential energy at the initial height (2 m) can be calculated using the formula:
\[ PE_{\text{initial}} = mgh \]
where:
- \( m \) = mass of the ball (we can keep it as \( m \) since it will cancel out later)
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \))
- \( h \) = height (2 m)

So,
\[ PE_{\text{initial}} = mg \times 2 \]

### Step 2: Calculate the potential energy after rebound (PE_final)
The potential energy after the ball rebounds to a height of 1.5 m can be calculated similarly:
\[ PE_{\text{final}} = mgh \]
where \( h = 1.5 \, \text{m} \):
\[ PE_{\text{final}} = mg \times 1.5 \]

### Step 3: Calculate the energy lost
The energy lost during the rebound can be calculated as:
\[ \text{Energy Lost} = PE_{\text{initial}} - PE_{\text{final}} \]
Substituting the values from Steps 1 and 2:
\[ \text{Energy Lost} = mg \times 2 - mg \times 1.5 \]
Factoring out \( mg \):
\[ \text{Energy Lost} = mg(2 - 1.5) = mg \times 0.5 \]

### Step 4: Calculate the percentage of energy lost
The percentage of energy lost can be calculated using the formula:
\[ \text{Percentage Loss} = \left( \frac{\text{Energy Lost}}{\text{Initial Energy}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Loss} = \left( \frac{mg \times 0.5}{mg \times 2} \right) \times 100 \]
The \( mg \) cancels out:
\[ \text{Percentage Loss} = \left( \frac{0.5}{2} \right) \times 100 = 25\% \]

### Final Answer
The percentage of energy lost is **25%**.

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