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Assertion: A body slides down an incline...

Assertion: A body slides down an inclined plane if the angle of friction is more than the angle of the inclined plane with the horizontal.
Reason : When the angle of inclination is equal to the angle of friction, the component of weight parallel to the plane is just sufficient to overcome the frictional force.

A

If both assertion `&` Reason are True `&` the Reason is a corrrect explanation of the Asserion.

B

If both Assertion `&` Reason are True but Reason is not correct explanation of the Assertion.

C

If Assertion is Trie but the Reason is False.

D

If both Assertion `&` Reason are false

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the assertion and reason provided in the question, we will break down the concepts of friction, inclined planes, and the conditions for sliding. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that a body slides down an inclined plane if the angle of friction (α) is greater than the angle of the inclined plane (θ). - To analyze this, we need to understand the relationship between the angle of friction and the angle of inclination. 2. **Condition for Sliding**: - A body will slide down the inclined plane if the component of gravitational force acting parallel to the incline exceeds the maximum static frictional force. - The maximum static frictional force can be expressed as \( F_{friction} = \mu_s N \), where \( \mu_s \) is the coefficient of static friction and \( N \) is the normal force. 3. **Forces Acting on the Body**: - The weight of the body can be resolved into two components: - Perpendicular to the incline: \( W \cos θ \) - Parallel to the incline: \( W \sin θ \) - The normal force \( N \) is equal to \( W \cos θ \). 4. **Frictional Force**: - The maximum frictional force that can act on the body is given by \( F_{friction} = \mu_s W \cos θ \). - The angle of friction (α) is related to the coefficient of static friction by \( \mu_s = \tan α \). 5. **Comparing Forces**: - For the body to slide, the condition is: \[ W \sin θ > F_{friction} \] which translates to: \[ W \sin θ > \mu_s W \cos θ \] - Simplifying gives: \[ \tan θ > \mu_s \] - Since \( \mu_s = \tan α \), we can rewrite this as: \[ \tan θ > \tan α \] - This implies that sliding occurs when \( θ > α \). 6. **Conclusion on Assertion**: - The assertion is incorrect because a body will slide down the inclined plane when the angle of inclination (θ) is greater than the angle of friction (α), not the other way around. 7. **Understanding the Reason**: - The reason states that when the angle of inclination is equal to the angle of friction, the component of weight parallel to the plane is just sufficient to overcome the frictional force. - This is correct because at this point, the forces are balanced, and the body is on the verge of sliding. 8. **Final Evaluation**: - The assertion is false, and the reason is true. Therefore, the correct conclusion is that the assertion does not support the reason.

To analyze the assertion and reason provided in the question, we will break down the concepts of friction, inclined planes, and the conditions for sliding. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that a body slides down an inclined plane if the angle of friction (α) is greater than the angle of the inclined plane (θ). - To analyze this, we need to understand the relationship between the angle of friction and the angle of inclination. ...
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