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Question

A block of mass 1 kg is placed on a rough inclined plane at an angle θ=60 with the horizontal and the block is connected with a string as shown in figure. If coefficient of friction between the block and inclined surface, μs=3/4, find the tension in the string. [Take g=10 m/s2]


A
0.66 N
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B
4.9 N
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C
5 N
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D
0 N
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Solution

The correct option is B 4.9 N

As block is placed on an inclined plane, block has a tendency to slide, therefore static friction comes into play and opposes the tendency of motion. The component of mg along the plane will be balanced by friction and tension force.

From the FBD,
N=mgcosθ
fmax=μsN=μsmgcosθ
=34×1×10×12
=3.75 N
and mgsinθ=1×10×32=53 N

Therefore the value of tension will be the difference of weight component and the maximum frictional force
mgsinθ=fmax+T
53=3.75+T
T=533.75
=4.9 N

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