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A body is in equilibrium under the influ...

A body is in equilibrium under the influence of a number of forces. Each has a different line of action. The minimum number of forces required is.

A

2, if their lines of action pass through the centre of mass of the body

B

3, if their lines of action are not parallel

C

3, if their lines of action are parallel

D

4, if their lines of action are parallel and all the forces have the same magnitude

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To solve the problem of determining the minimum number of forces required for a body to be in equilibrium when each force has a different line of action, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding Equilibrium**: A body is said to be in equilibrium when the net force and net torque acting on it are both zero. This means that the sum of all forces acting on the body must balance out. 2. **Considering Forces**: When forces act on a body, they can be represented as vectors. The minimum number of forces required for equilibrium depends on their lines of action and their magnitudes. 3. **Two Forces**: If we consider two forces acting on a body, if they are not equal in magnitude and act along different lines of action, they will create a resultant force that is not zero. Therefore, two forces alone cannot maintain equilibrium if they are not equal and opposite. 4. **Three Forces**: Introducing a third force can help achieve equilibrium. If three forces are acting on a body and they are not parallel, it is possible for them to balance each other out. Specifically, if the three forces are arranged such that they form a closed triangle (i.e., they are in equilibrium), then the body can be in equilibrium. 5. **Conclusion**: The minimum number of forces required for a body to be in equilibrium, considering that they have different lines of action, is **three**. This is because two forces cannot achieve equilibrium unless they are equal and opposite, which is not the case here since the problem states that each force has a different line of action. ### Final Answer: The minimum number of forces required for a body to be in equilibrium, with each force having a different line of action, is **three**. ---
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