two particles A and B each of mass m are connected by a massless string A is placed on - Physics - Gravitation

Question

two particles A and B each of mass m are connected by a massless
string A is placed on a rough table The string passes over a small
, smooth peg B is left from a position making angle theta with the
vertical If the minimum coeffient of friction between A and table
is umin=3-Ncostheta so that A does not slip during the
motion of mass B then calculate the value of N

Ved Prakash Lakhera · Accepted Answer

Masses are placed as shown in the diagram
In balancing condition following are the eqns of motion
ma =Tsinθ---1  mg=Tcosθ ---2and    R = mg---3         T = (3-N cosθ)R = (3-N cosθ)mg---4from eqns 2 and 4, we get,mgcosθ =  (3-N cosθ)mgor     1 = 3 cosθ-N cos2θor    N =3cosθ-1 cos2θ = 3 secθ -sec2θ