CBSE Class 11-science Answered

Let the maximum force, which the man can exert be F acting at an angle θ. Now, breaking the rectangular components of 'F' along the horizontal and vertical direction: 

(i) F cos  θ in horizontal direction

(ii) F sin θ in vertical directioon.

Also, the weight of the body mg acts in vertically downward direction,

So, F sin θ + R = mg

or, R = mg - F sin θ.

The force of limiting friction, f = μ R = μ ( mg - F sin θ )

Now as long as 'F cosθ' is less than 'f' , acceleration is zero; which means the maximum force the man can exert

F cosθ < μ ( mg - F sin θ )

or,

F_max  < [μ ( mg - F sin θ )] / cos θ