A meter scale of mass `400 gm` is lying horizontally on the floor. If it is to be held vertically with one end touching the floor, the work to be done is

Options

A. `6 J`
B. `4 J`
C. `40 J`
D. `2J`

Explanation

To solve the problem of calculating the work done to lift a meter scale from a horizontal position to a vertical position, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Mass and Length of the Scale**:
- The mass of the meter scale is given as \( m = 400 \, \text{g} = 0.4 \, \text{kg} \).
- The length of the scale is \( L = 1 \, \text{m} \).

2. **Determine the Initial Position of the Center of Mass**:
- When the scale is lying horizontally, the center of mass is at the midpoint of the scale.
- Therefore, the initial height of the center of mass is:
\[ h_i = 0 \, \text{m} \]

3. **Determine the Final Position of the Center of Mass**:
- When the scale is held vertically, the center of mass is still at the midpoint, but now it is raised to a height of:
\[ h_f = \frac{L}{2} = \frac{1 \, \text{m}}{2} = 0.5 \, \text{m} \]

4. **Calculate the Change in Height**:
- The change in height (\( \Delta h \)) of the center of mass when moving from the initial position to the final position is:
\[ \Delta h = h_f - h_i = 0.5 \, \text{m} - 0 \, \text{m} = 0.5 \, \text{m} \]

5. **Calculate the Work Done Against Gravity**:
- The work done against gravity can be calculated using the formula for gravitational potential energy:
\[ W = mgh \]
- Substituting the values:
\[ W = (0.4 \, \text{kg}) \times (9.8 \, \text{m/s}^2) \times (0.5 \, \text{m}) \]
- Calculating this gives:
\[ W = 0.4 \times 9.8 \times 0.5 = 1.96 \, \text{J} \]

6. **Final Answer**:
- The work done to lift the meter scale from a horizontal position to a vertical position is approximately:
\[ W \approx 2 \, \text{J} \quad (\text{rounding to two significant figures}) \]