A 5 kg brick of dimensions `20cmxx10cmxx8cm` is lying on the largest base. It is now made to stand with length vertical. If `g=10m//s^(2)`, then the amount of work done is

Options

A. 3J
B. 5J
C. 7J
D. 9J

Explanation

To solve the problem of calculating the work done in changing the position of the brick, we will follow these steps:

### Step 1: Understand the Initial Position of the Brick
The brick has dimensions 20 cm x 10 cm x 8 cm and is lying on its largest base (20 cm x 10 cm). Therefore, the height of the center of mass (COM) when lying down is half of its height (8 cm).

**Hint:** The center of mass for a uniform rectangular object is located at its geometric center.

### Step 2: Calculate the Initial Height of the Center of Mass
The initial height of the center of mass (H_initial) when the brick is lying down is:
\[ H_{\text{initial}} = \frac{\text{height}}{2} = \frac{8 \text{ cm}}{2} = 4 \text{ cm} = 0.04 \text{ m} \]

**Hint:** Remember to convert cm to meters for consistency with SI units.

### Step 3: Calculate the Initial Potential Energy
Using the formula for gravitational potential energy (PE):
\[ PE_{\text{initial}} = mgh \]
Where:
- \( m = 5 \text{ kg} \)
- \( g = 10 \text{ m/s}^2 \)
- \( h = H_{\text{initial}} = 0.04 \text{ m} \)

Calculating:
\[ PE_{\text{initial}} = 5 \text{ kg} \times 10 \text{ m/s}^2 \times 0.04 \text{ m} = 2 \text{ J} \]

**Hint:** This energy represents the potential energy when the brick is lying flat.

### Step 4: Understand the Final Position of the Brick
When the brick is made to stand vertically, the height of the center of mass (H_final) is now at half of its new height (10 cm).

**Hint:** The center of mass will shift when the orientation of the brick changes.

### Step 5: Calculate the Final Height of the Center of Mass
The final height of the center of mass (H_final) when the brick is standing is:
\[ H_{\text{final}} = \frac{10 \text{ cm}}{2} = 5 \text{ cm} = 0.05 \text{ m} \]

**Hint:** Again, ensure to convert cm to meters.

### Step 6: Calculate the Final Potential Energy
Using the same potential energy formula:
\[ PE_{\text{final}} = mgh \]
Where:
- \( h = H_{\text{final}} = 0.05 \text{ m} \)

Calculating:
\[ PE_{\text{final}} = 5 \text{ kg} \times 10 \text{ m/s}^2 \times 0.05 \text{ m} = 2.5 \text{ J} \]

**Hint:** This energy represents the potential energy when the brick is standing upright.

### Step 7: Calculate the Work Done
Using the work-energy principle:
\[ \text{Work Done} = PE_{\text{final}} - PE_{\text{initial}} \]
Calculating:
\[ \text{Work Done} = 2.5 \text{ J} - 2 \text{ J} = 0.5 \text{ J} \]

**Hint:** Work done is the change in potential energy as the position of the object changes.

### Final Answer
The amount of work done in making the brick stand upright is **0.5 Joules**.