A lift is tied with thick iron ropes having mass ‘M’. The maximum acceleration of the lift is ‘a’ m / s 2 and maximum safe stress is ‘S’ N / m 2 . The minimum diameter of the rope is

Question

A lift is tied with thick iron ropes having mass ‘M’. The maximum acceleration of the lift is ‘a’ m / s 2 and maximum safe stress is ‘S’ N / m 2 . The minimum diameter of the rope is, 6 M g + a π S 1 2, 4 M g + a π S 1 2, M g + a π S 1 2, M g - a π S 1 2

MARKS App · Accepted Answer

The maximum stress produced in a rope is given by σ m a x = F o r c e A r e a = M g π r 2 As the lift is accelerating with acceleration a, then σ m a x = M g ± a π r 2 ⇒ r 2 = M g ± a π S [Given, σ m a x = S ] d 2 4 = M g ± a π S ∵ r = d 2 ⇒ d = 4 M g ± a π S As acceleration is maximum i.e.’=g +a, so d = 4 M g + a π S

Search any question & find its solution

Looking for more such questions to practice?