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Question

A block begins to slide down a rough inclined plane of angle 45 and moves 1 m in 42 s. What is the coefficient of friction μ, between the plane and the block?
(Take g=10 m/s2)

A
0.4
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B
0.5
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C
0.6
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D
0.8
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Solution

The correct option is D 0.8
Let a be the acceleration of the block down the inclined plane. The given question can be depicted as shown below

The coefficient of friction between the block and the incline plane is μ
Now, from the FBD we have
mgsin45f=ma......(1)
and, N=mgcos45
Friction force, f=μN=μmgcos45
On putting the value of f in eq (1) we get
mgsin45μmgcos45=ma
a=g(sin45μcos45)=10(1μ)2 m/s2

Using the equation of motion
s=ut+12at2
1=0+12×10(1μ)2×(42)2μ=0.8

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