Question
Download Solution PDFA particle of mass 1 kg resting on rough contact with a plane inclined at 30° to the horizontal is just about to slip. The coefficient of friction between the plane and the particle will be
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
When a body is just about to slip on an inclined plane, the condition of limiting equilibrium applies. The frictional force is at its maximum, and we use the relation:
\( \mu = \tanθ \)
Calculation:
Given:
- Mass m = 1 kg
- Inclination θ = 30∘
On an inclined plane:
- Normal reaction: \( N = mg \cosθ \)
- Downslope force: \( mg \sinθ \)
At limiting equilibrium, friction balances the downslope force:
\( mg \sinθ = \mu mg \cosθ \)
\( \Rightarrow \mu = \frac{\sinθ}{\cosθ} = \tanθ \)
\( \mu = \tan 30^∘ = \frac{1}{\sqrt{3}} \)
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