Q.

A lift is tied with thick iron and its mass is 314 kg. What should be the minimum diameter of wire if the maximum acceleration of lift is 1.2 m/sec2 and the maximum safe stress of the wire is 1 x 107 N/m2?

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a

2 cm

b

1 cm

c

1.5 cm

d

none of these

answer is A.

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Detailed Solution

The tension, T in the rope of the lift when it goes upward is given byT = m(g+a) = 314×11NLet r be the radius of the wire, then maximum stress will be Tπr2Hence, Tπr2 = 1.1×107or  r2 = Tπ×1.4×108 = 314×113.14×(1.1×107) = 1104Now  r = 1102m = 1 cm∴ Diameter of the wire = 2r = 2cm.
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A lift is tied with thick iron and its mass is 314 kg. What should be the minimum diameter of wire if the maximum acceleration of lift is 1.2 m/sec2 and the maximum safe stress of the wire is 1 x 107 N/m2?