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A lift is tied with thick iron and its m...

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)/(sec^2)` and the maximum safe stress of the wire is `1xx10^7(N)/(m^2)`?

A

4

B

5

C

6

D

7

Text Solution

Verified by Experts

The correct Answer is:
B
When the lift moves up with maximum acceleration, the tension T = m (g + a) = 1000 (9.8 + 1.2) = 11000 N
The stress in the wire = Tension per unit area `= (T)/(pi r^(2))`
Let r be the maximum radius of the wire, for maximum safe stress of `1.4 xx 10^(8) N//m^(2)`
`:. 1.4 xx 10^(8) = (T)/(pi r^(2)) = (11000)/(pi r^(2))`
`:. r^(2) = (11000)/((22)/(7) xx 1.4 xx 10^(8)) = 0.25 xx 10^(-4)`
`:. r = 0.5 xx 10^(-2) m = 5 xx 10^(-3) m = 5 mm`
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