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Assertion: Three concurrent force are F(...

Assertion: Three concurrent force are `F_(1),F_(2)` and `F_(3)`. Angle between `F_(1)` and `F_(2)` is `30^(@)`and between `F_(1)` and `F_(3)` is `120^(@)`. Under these conditions forces cannot remain in equilibrium.
Reason: At least one angle should be greater then `180^(@)`.

A

If both Accertion and Reason are true and the reason is correct explanation of the Assertion.

B

If both Accertion and Reason are true but reason is not the correct explanation of Assertion.

C

If Assertion is true, but the Reason is false.

D

If Assertion is false but the Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the assertion and the reason provided in the question. ### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that three concurrent forces \( F_1, F_2, \) and \( F_3 \) cannot remain in equilibrium given the angles between them. Specifically, the angle between \( F_1 \) and \( F_2 \) is \( 30^\circ \) and the angle between \( F_1 \) and \( F_3 \) is \( 120^\circ \). 2. **Visualizing the Forces**: - Let \( F_1 \) be directed along the positive x-axis. - The force \( F_2 \) makes an angle of \( 30^\circ \) with \( F_1 \) (i.e., it is directed at \( 30^\circ \) from the x-axis). - The force \( F_3 \) makes an angle of \( 120^\circ \) with \( F_1 \) (i.e., it is directed at \( 120^\circ \) from the x-axis). 3. **Analyzing the Angles**: - The angle between \( F_1 \) and \( F_2 \) is \( 30^\circ \). - The angle between \( F_1 \) and \( F_3 \) is \( 120^\circ \). - The angle between \( F_2 \) and \( F_3 \) can be calculated as follows: \[ \text{Angle between } F_2 \text{ and } F_3 = 180^\circ - (30^\circ + 120^\circ) = 30^\circ. \] 4. **Condition for Equilibrium**: For three forces to be in equilibrium, they must satisfy the condition that the vector sum of the forces equals zero. This can be achieved if the angles between the forces allow for a balance of magnitudes and directions. 5. **Evaluating the Reason**: The reason states that at least one angle should be greater than \( 180^\circ \) for equilibrium to be possible. This is not a correct statement. In fact, for three forces to be in equilibrium, the sum of the angles between them must be \( 360^\circ \), and no angle should exceed \( 180^\circ \). 6. **Conclusion**: Since the angles between the forces do not allow for equilibrium (as they sum to \( 360^\circ \) without exceeding \( 180^\circ \)), the assertion is true. However, the reason provided is incorrect. Therefore, the assertion is true, but the reason is not a correct explanation of the assertion. ### Final Answer: - Both assertion and reason are not correct together. The assertion is true, but the reason is false.

To solve the problem, we need to analyze the assertion and the reason provided in the question. ### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that three concurrent forces \( F_1, F_2, \) and \( F_3 \) cannot remain in equilibrium given the angles between them. Specifically, the angle between \( F_1 \) and \( F_2 \) is \( 30^\circ \) and the angle between \( F_1 \) and \( F_3 \) is \( 120^\circ \). 2. **Visualizing the Forces**: - Let \( F_1 \) be directed along the positive x-axis. ...
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