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Question

A coin is pushed down tangentially from an angular position θ on a circular surface, with velocity v as shown. If the cofficient of friction between the coin and surface is μ, find the tangential acceleration of the coin.


A
gsinθ
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B
gsinθμgcosθ
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C
gsinθμgcosθμv2/R
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D
gsinθμv2/R
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Solution

The correct option is C gsinθμgcosθμv2/R

FBD of coin is shown above.
As coin slides down, friction acts along the plane.
Therefore, in radial direction:
Nmgcosθ=mv2/R
N=[mv2/R+mgcosθ](i)
In tangential direction:
(mgsinθ)f=mat
mat=mgsinθμN (kinetic friction f=μN)
Substituting (i)
mat=mgsinθμ[mv2R+mgcosθ]
at=gsinθμv2Rμgcosθ

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