Two weights of 7 kg and 9 kg are hanging through the end-points of a 8m light wire. The centre of mass of this system, from 7 kg weight, is at a distance of

Options

A. 4.5 m
B. 3.5 m
C. 5.0 m
D. 3 m

Explanation

To find the center of mass of the system consisting of two weights (7 kg and 9 kg) hanging from the ends of an 8-meter light wire, we can follow these steps:

### Step 1: Understand the System
We have two weights:
- Weight 1 (W1) = 7 kg (hanging at one end of the wire)
- Weight 2 (W2) = 9 kg (hanging at the other end of the wire)

The total length of the wire is 8 meters.

### Step 2: Define the Positions
Let's define the position of the 7 kg weight as the origin (0 m). Therefore:
- Position of 7 kg weight (W1) = 0 m
- Position of 9 kg weight (W2) = 8 m

### Step 3: Use the Formula for Center of Mass
The center of mass (CM) for a system of particles can be calculated using the formula:
\[ CM = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \]
where:
- \(m_1\) and \(m_2\) are the masses,
- \(x_1\) and \(x_2\) are their respective positions.

### Step 4: Substitute the Values
Substituting the values into the formula:
\[ CM = \frac{(7 \, \text{kg} \cdot 0 \, \text{m}) + (9 \, \text{kg} \cdot 8 \, \text{m})}{7 \, \text{kg} + 9 \, \text{kg}} \]

### Step 5: Calculate the Numerator and Denominator
Calculating the numerator:
\[ CM = \frac{0 + 72}{16} = \frac{72}{16} \]

Calculating the denominator:
\[ 7 + 9 = 16 \]

### Step 6: Simplify the Expression
Now, simplifying the expression:
\[ CM = \frac{72}{16} = 4.5 \, \text{m} \]

### Step 7: Conclusion
The center of mass of the system from the 7 kg weight is at a distance of 4.5 meters.