A body of mass 10kg slides along a rough horizontal surface. The coefficient of friction is 1/3 Taking g=10m/s2, the least force which acts at an angle of 300 to the horizontal is ___N.

Let P fore is acting at an angel 300 with the horizontal. For the condition of motion F = μR P cos300 = μ(mg – P sin300)⇒P32=13(100−P12)⇒3P2=(100−P2)⇒2P=100⇒P=50N

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A body of mass 10kg slides along a rough horizontal surface. The coefficient of friction is $1 / \sqrt{3}$ Taking g=10m/s², the least force which acts at an angle of 30⁰to the horizontal is ___N.

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answer is 50.

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Detailed Solution

Let P fore is acting at an angel 30⁰with the horizontal. For the condition of motion F = μR
P cos30⁰ = μ(mg – P sin300)
$\Rightarrow P \frac{\sqrt{3}}{2} = \frac{1}{\sqrt{3}} (100 - P \frac{1}{2}) \Rightarrow \frac{3 P}{2} = (100 - \frac{P}{2})$
$\Rightarrow 2 P = 100 \Rightarrow P = 50 N$