GATE 2024 MN – Question 63
Replace a winding rope in the shown 1.2 m drum/sheave system. Shaft depth 215 m, headgear 32 m, slope span 45.5 m and sheave contact 120°. Allow 1 m anchorage, at least two drum turns at bottom landing, and 2 m cut off per six-month recapping over maximum life 3.5 years. No overwind or fleet-angle correction. Find minimum new rope length in m, to two decimals.
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Correct answer: 313.00 to 316.00
Explanation
Straight running lengths total 215+32+45.5=292.5 m. Sheave contact adds(120/360)π×1.2=1.2566 m; two reserve turns add 2π×1.2=7.5398 m; anchorage adds 1 m. Six recappings before final retirement add 12 m. Total 314.296 m, or 314.30. A seventh cut at the retirement instant is not required.