Answer :


Let us consider the force F is applied on the body which is making angle θ with horizontal.


From the free body diagram,
R + F sin θ = mg
R = −F sin θ + mg (1)
μR = F cos θ (2)


From Equation (1),
μ(mgFsin θ)−F cos θ = 0
μmg = μF sin θ +F cos θ



The applied force F should be minimum, when μ sin θ + cos θ is maximum.
Again, μ sin θ + cos θ is maximum when its derivative is zero:


d/dθ (μsin θ+ cos θ) =0


μ cos θ − sin θ = 0
θ = tan−1 μ
So,



Dividing numerator and denominator by cos θ, we get


Therefore, the minimum force required is


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