Two smooth cylindrical bars weighing W N each lie next to each other in contact. A similar third bar is placed over the two bars as shown in figure. Neglecting friction, if the minimum horizontal force (in N) on each lower bar necessary to keep them in contact is F, find F. (Take W = 10√3 N)
Physics · Mixed Chapter
JEE Mains

Question

Two smooth cylindrical bars weighing W N each lie next to each other in contact. A similar third bar is placed over the two bars as shown in figure. Neglecting friction, if the minimum horizontal force (in N) on each lower bar necessary to keep them in contact is F, find F. (Take W = 10√3 N)

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The centres of the three touching identical cylinders form an equilateral triangle; each inclined line of contact makes 60° with the horizontal. Step 2: For the upper bar (weight W), the two equal normal reactions N satisfy 2N sin60°=W, giving N=W/√3. Step 3: Each lower bar receives outward horizontal thrust N cos60°=W/(2√3). That is the minimum horizontal force F needed on each lower bar. Step 4: With W=10√3 N, F=10√3/(2√3)=5 N. Answer: 5.