Find the least pulling force acting at an angle of 30∘ with the horizontal, which can just slide a body of mass 10kg along a rough horizontal surface [μs=μk=1√3,g=10m/s2]
A
25N
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B
75N
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C
50N
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D
100N
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Solution
The correct option is C50N 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(10g−Psin30∘)−−(2)
From (1) and (2), Pcos30∘=μk(100−Psin30∘) P(cos30∘+μksin30∘)=μk(100) P=μk×100cos30∘+μksin30∘ =100√3√32+12√3 =2004=50N