masses of 3,5,7,8 kg are suspended at equal distances of 1 m from rod.Find the CG of the arrangement.

To find the Center of Gravity (CG) of the given arrangement, we need to calculate the weighted average of the masses with respect to their distances from the rod.

The Center of Gravity is the point where the resultant weight of the system acts vertically downward, regardless of the arrangement's orientation. In this case, we can assume the rod is horizontal.

To find the CG, we multiply each mass by its respective distance from the rod, then sum them up, and divide the result by the total sum of the masses.

Let's calculate it step by step:

1. Assign the given masses and distances to variables:
- Mass 1 (m1) = 3 kg
- Mass 2 (m2) = 5 kg
- Mass 3 (m3) = 7 kg
- Mass 4 (m4) = 8 kg
- Distance from rod:
- Distance 1 (d1) = 1 m
- Distance 2 (d2) = 1 m
- Distance 3 (d3) = 1 m
- Distance 4 (d4) = 1 m

2. Calculate the weighted sum of masses by multiplying each mass by its respective distance:
- Weighted sum = (m1 * d1) + (m2 * d2) + (m3 * d3) + (m4 * d4)

Calculate each term separately:
- Term 1 = 3 kg * 1 m
- Term 2 = 5 kg * 1 m
- Term 3 = 7 kg * 1 m
- Term 4 = 8 kg * 1 m

Summing them up:
- Weighted sum = (3 kg * 1 m) + (5 kg * 1 m) + (7 kg * 1 m) + (8 kg * 1 m)

3. Calculate the total mass of the system:
- Total mass (m_total) = m1 + m2 + m3 + m4

Calculate it:
- m_total = 3 kg + 5 kg + 7 kg + 8 kg

4. Finally, calculate the Center of Gravity (CG) using the weighted sum and total mass:
- CG = Weighted sum / m_total

Plug in the values:
- CG = (3 kg * 1 m + 5 kg * 1 m + 7 kg * 1 m + 8 kg * 1 m) / (3 kg + 5 kg + 7 kg + 8 kg)

Compute the values and you will find the CG of the arrangement.