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Question

In figure, a crate slides down an inclined right-angled trough. The coefficient of kinetic friction between the crate and the trough is μk. What is the acceleration of the crate in terms of μk,θ and g?

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A
g(sinθ2μkcosθ)
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B
g(sinθμkcosθ2)
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C
g(sinθ+2μkcosθ)
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D
g(sinθ+μkcosθ2)
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Solution

The correct option is A g(sinθ2μkcosθ)
The force of gravity is acting downwards
Resolving gravitation force in inclination plane
along incline plane mgsinθf=ma..(i)
perpendicular to incline plane N1+N22=mgcosθ...(ii)
The kinetic friction is given by f=2μkmgcosθ...(iii)
Substituting value of f in equation (i)
a=g(sinθ2μkcosθ)

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