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Question

Find the least pulling force acting at an angle of 30 with the horizontal, which can just slide a body of mass 10 kg along a rough horizontal surface [μs=μk=13, g=10 m/s2]

A
25 N
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B
75 N
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C
50 N
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D
100 N
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Solution

The correct option is C 50 N
From the FBD of body

Along horizontal direction,
f=Pcos30(1)
Along vertical direction,
R+Psin30=10g

When body is just sliding,
f=μkR=μk(10gPsin30)(2)

From (1) and (2),
Pcos30=μk(100Psin30)
P(cos30+μksin30)=μk(100)
P=μk×100cos30+μksin30
=100332+123
=2004=50 N

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