A string is connected to block of mass m = 1.2 kg placed over rough table surface as shown in figure. Calculate minimum vertical force F (in newton) required to move the block. Pulley and string are ideal and coefficient of friction between block and table surface is μ = 1/2; take g = 10 m/s².
Physics · Mixed Chapter
JEE Mains

Question

A string is connected to block of mass m = 1.2 kg placed over rough table surface as shown in figure. Calculate minimum vertical force F (in newton) required to move the block. Pulley and string are ideal and coefficient of friction between block and table surface is μ = 1/2; take g = 10 m/s².

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Let the common tension in the ideal string be T. At the lower knot, two equal tensions act symmetrically at 37° from vertical; thus F=2Tcos37°=(8/5)T. Step 2: The block feels a horizontal rightward force T+Tsin37°=(8/5)T, while the diagonal string pulls down with Tcos37°=(4/5)T. Step 3: Its normal reaction is N=mg+(4/5)T=12+(4/5)T, so limiting friction is μN=6+(2/5)T. Step 4: At impending motion, (8/5)T=6+(2/5)T, giving T=5 N. Step 5: Minimum F=(8/5)×5=8 N.