Deformation of a Bar under its own weight vs Direct Load

Deformation refers to the change in shape or size of an object when a force is applied to it. The amount of deformation depends on various factors, including the type of material, the magnitude of the force, and the direction of the force.

When a bar is subjected to its own weight, it experiences a certain amount of deformation. This is because the weight of the bar exerts a force on it, causing it to bend or sag. The amount of deformation in this case depends on the length of the bar, its cross-sectional area, and the material it is made of.

On the other hand, if the same bar is subjected to a direct load equal to its weight, it will experience a different amount of deformation. In this case, the force acting on the bar is equal to its weight, but it is applied in a different direction. The amount of deformation in this case depends on the same factors as before, as well as the angle at which the force is applied.

Answer Explanation

The correct answer is option B, which states that the deformation of a bar under its own weight is half the deformation if the same body is subjected to a direct load equal to the weight of the body. This is because:

- When the bar is subjected to its own weight, the force acting on it is distributed evenly along its length. This means that the deformation is spread out over the entire length of the bar.
- When the same bar is subjected to a direct load equal to its weight, the force acting on it is concentrated at a single point or a few points, depending on the direction of the force. This means that the deformation is concentrated at these points, resulting in a greater amount of deformation.
- Therefore, the deformation of the bar under its own weight is less than the deformation when it is subjected to a direct load equal to its weight. In fact, it is half of the deformation in the latter case, as stated in option B.

Conclusion

In conclusion, the amount of deformation in a bar depends on various factors, including the type of material, the magnitude of the force, and the direction of the force. When a bar is subjected to its own weight, it experiences a certain amount of deformation, which is less than the deformation when it is subjected to a direct load equal to its weight. The correct answer is option B, which states that the deformation of a bar under its own weight is half the deformation if the same body is subjected to a direct load equal to the weight of the body.