A total of 4900 joule was expended in lifting a 50 kg mass. The mass was raised to a height of

Options

A. 98 m
B. 960 m
C. 245 m
D. 10 m

Answer

To solve the problem of lifting a 50 kg mass with an expenditure of 4900 joules, we can use the formula for gravitational potential energy. The potential energy (PE) gained when an object is lifted to a height (h) is given by the equation:

\[ PE = m \cdot g \cdot h \]

Where:
- \( PE \) is the potential energy (in joules),
- \( m \) is the mass (in kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( h \) is the height (in meters).

### Step 1: Write down the given information
- Total energy expended (PE) = 4900 joules
- Mass (m) = 50 kg
- Acceleration due to gravity (g) = 9.8 m/s²

### Step 2: Set up the equation for potential energy
Using the formula for potential energy, we can set up the equation:

\[ 4900 = 50 \cdot 9.8 \cdot h \]

### Step 3: Solve for height (h)
To find the height \( h \), we rearrange the equation:

\[ h = \frac{4900}{50 \cdot 9.8} \]

### Step 4: Calculate the denominator
First, calculate \( 50 \cdot 9.8 \):

\[ 50 \cdot 9.8 = 490 \]

### Step 5: Substitute back to find h
Now substitute back into the equation for \( h \):

\[ h = \frac{4900}{490} \]

### Step 6: Perform the division
Now, perform the division:

\[ h = 10 \, \text{meters} \]

### Conclusion
The height to which the 50 kg mass was raised is **10 meters**.

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