# A block of mass M

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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

A rectangular boxPhysics - Exemplar

A helicopter of mPhysics - Exemplar

There are four foPhysics - Exemplar

When a body <spanPhysics - Exemplar

Block <span lang=Physics - Exemplar

A block <span lanPhysics - Exemplar

Two <span lang="EPhysics - Exemplar