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Question:

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10N. The coefficient of static friction between the block and the plane is : [Take g=10m/s²]

√32

23

14

√34

Solution:

From the free body diagram
ΣF=0
2+mgsin30° = μmgcos30° (i)
10=mgsin30°+μmgcos30° (ii)
Adding eq(i) and (ii), we get
12=2μmgcos30°
6=μmgcos30°.. (iii)
4=mgsin30° (iv)
From eqn(iii) and (iv), we get
32=μ × cot30°
32=μ × √3
μ = 3/(2√3) = √3/2