A uniform rope of mass hangs from a ceiling and carries a block of mass at its lower end. The system is pulled upward by the ceiling support so that it accelerates upward at . Taking , the tension in the rope at a point one-quarter of its length from the top is
Answer and explanation
Correct answer: D.
- Step 1: The tension at any cross section of the rope must support and accelerate all the mass hanging below that point.
- Step 2: At a point one-quarter length from the top, three-quarters of the rope length hangs below, with mass . Adding the attached block mass (), total mass below is .
- Step 3: Apply Newton's second law for upward acceleration: .
Answer
.
Why not the others: calculates only the static weight without upward acceleration, while is the tension at the ceiling.
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