Two laborers A&B carry a uniform pole of weight 50N .if the pole is 2M long .find the reactions at A&B . given that each laborers is 10 cm from each end.?

To find the reactions at points A and B, we need to consider the forces acting on the pole. Since the pole is uniform and the weight is evenly distributed, the weight of the pole can be considered to act at its center of gravity, which is at the midpoint of the pole.

Let's denote the reactions at points A and B as Ra and Rb, respectively. Since the pole is in equilibrium, the sum of the vertical forces acting on the pole must be zero.

Sum of forces in the vertical direction:
Ra + Rb - 50N = 0

Since the pole is symmetrical, the reactions at points A and B will be equal. Let's denote this reaction force as R:

Ra = R
Rb = R

Substitute these values back into the equation:

R + R - 50N = 0
2R - 50N = 0
2R = 50N
R = 25N

Therefore, the reactions at points A and B are both 25N.

Given:

- Weight of pole, W = 50N
- Length of pole, L = 2m = 200cm
- Distance of A and B from the ends = 10cm

To find:

- Reactions at A and B

Solution:

The pole is in equilibrium under the action of the weight and the reactions at A and B.

Let R_A be the reaction at A and R_B be the reaction at B.

Taking moments about A:

```
R<sub>B</sub> x L - W x (L/2) = 0
```

Substituting values:

```
R<sub>B</sub> x 200 - 50 x 100 = 0
```

```
R<sub>B</sub> = 25N
```

Taking moments about B:

```
R<sub>A</sub> x L - W x (L/2) = 0
```

Substituting values:

```
R<sub>A</sub> x 200 - 50 x 100 = 0
```

```
R<sub>A</sub> = 25N
```

Therefore, the reactions at A and B are both 25N.