An ant sitting on a string can pull the string with a maximum force up to three times of its own weight. A sine wave of amplitude A=10/π² in vertical plane is generated in the string. Find the least time period of oscillations of string elements so that ant will not fall from the string. (Neglect the variation of tension in the string due to weight of the ant; g=10 m/s².)
Physics · Mixed Chapter
JEE Mains

Question

An ant sitting on a string can pull the string with a maximum force up to three times of its own weight. A sine wave of amplitude A=10/π² in vertical plane is generated in the string. Find the least time period of oscillations of string elements so that ant will not fall from the string. (Neglect the variation of tension in the string due to weight of the ant; g=10 m/s².)

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: A point on the rope performing SHM has a maximum vertical acceleration Aω². For the ant to remain attached, its maximum required grip cannot exceed 3mg. Step 2: At the maximum upward acceleration point, required hold is m(g+Aω²), so set m(g+Aω²)≤3mg. This gives Aω²≤2g. Step 3: The minimum allowed period is T_min=2π√(A/(2g))=2π√[(10/π²)/(20)]=√2 s≈1.414 s. Step 4: The printed numerical key is 1, consistent with taking the nearest integer to √2; the question does not explicitly request ro…