A lift is tied with thick iron ropes having mass ' M '. The maximum acceleration of the lift is ' a ' m/s² and maximum safe stress is ' S ' N/m². The minimum diameter of the rope is (a) [(6M(g+a))/(π S)]1/2 (b) [(4M(g+a))/(π S)]1/2 (c) [(M(g+a))/(π S)]1/2 (d) [(M(g-a))/(π S)]1/2

Answer: (b). Maximum tension in the rope (lift accelerating up): T = M(g + a). Safe stress: S = (T)/(π d²/4) d = [(4M(g+a))/(π S)]1/2 So the answer is (b).

A lift is tied with thick iron ropes having mass ' M '. The maximum… | MHT CET 2019 (2 May, Shift 2)

Q15MHT CET 2019 · 2 MAY · SHIFT 2Medium

Thermal Stress & Breaking Stress

A lift is tied with thick iron ropes having mass ' $M$ '. The maximum acceleration of the lift is ' $a$ ' $\text{m/s}^2$ and maximum safe stress is ' S ' $\text{N/m}^2$ . The minimum diameter of the rope is

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Answer: (b)

Maximum tension in the rope (lift accelerating up): $T = M(g + a)$ .
Safe stress: $S = \dfrac{T}{\pi d^2/4}$
$d = \left[\dfrac{4M(g+a)}{\pi S}\right]^{1/2}$
So the answer is (b).

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