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Question

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


A

g(sin - cos )

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B

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C

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D

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Solution

The correct option is D


As the coin slides down, friction is kinetic and acts up along the plane.

Equation of motion : Fr=Nmg cosθ=mar ........... (i)

Ft=mg sinθfk=mat ........... (ii)

But fk=μN ........... (iii)

And centripetal acceleration is ar = mv2R ........... (iv)

Substituting fk from equation (iii), in equation (ii),

We get at=g sinθμNm ...........(v)

Now, substituting N from equation (i) in equation (v), we get at=g(sinθμcosθ)μv2R


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