The work done in lifting a mass of 1 kg to a height of 9.8 m is

Options

A. 1 J
B. `(9.8)^(2)` J
C. 9.8 J
D. none of these

Answer

To find the work done in lifting a mass of 1 kg to a height of 9.8 m, we can follow these steps:

### Step 1: Understand the Concept of Work Done
Work done (W) is defined as the product of the force (F) applied and the displacement (s) in the direction of the force. The formula for work done is:
\[ W = F \cdot s \cdot \cos(\theta) \]
where:
- \( W \) is the work done,
- \( F \) is the force applied,
- \( s \) is the displacement,
- \( \theta \) is the angle between the force and the displacement.

### Step 2: Identify the Force Required to Lift the Mass
When lifting an object against gravity, the force applied must equal the weight of the object. The weight (W) can be calculated using the formula:
\[ F = m \cdot g \]
where:
- \( m \) is the mass (1 kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).

So, for a mass of 1 kg:
\[ F = 1 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 9.8 \, \text{N} \]

### Step 3: Calculate the Work Done
Now that we have the force, we can calculate the work done in lifting the mass to a height of 9.8 m. The displacement \( s \) is 9.8 m and the angle \( \theta \) is 0 degrees (since the force and displacement are in the same direction). Therefore, \( \cos(0) = 1 \).

Using the work done formula:
\[ W = F \cdot s \cdot \cos(0) \]
Substituting the values:
\[ W = 9.8 \, \text{N} \cdot 9.8 \, \text{m} \cdot 1 \]
\[ W = 9.8 \cdot 9.8 \]
\[ W = 96.04 \, \text{J} \]

### Step 4: Round the Answer
For practical purposes, we can round this to approximately:
\[ W \approx 98 \, \text{J} \]

### Final Answer
The work done in lifting a mass of 1 kg to a height of 9.8 m is approximately **98 Joules**.

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