A body of mass 10kg is on a rough inclined plane having an inclination of $30^{0}$ with the horizontal. If coefficient of friction between the surfaces of contact of the body and the plane is 0.5 ,then find the least force required to pull the body up the plane.

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91.4N

85.4N

78.4N

80.5N

answer is B.

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Detailed Solution

F = m g (\sin θ + μ_{k} \cos θ) = 10 \times 9.8 (\frac{1}{2} + \frac{1}{2} \frac{\sqrt{3}}{2})

$= \frac{10 \times 9.8}{2} (1 + \frac{\sqrt{3}}{2}) = 49 (1 + \frac{1.732}{2})$
$= 49 \times 1.866 = 91.434$

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