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A polyester fibre rope of diameter 3 cm ...

A polyester fibre rope of diameter 3 cm has a breaking strength of 150 kN. If it is required to have 600 kN breaking strength. What should be the diameter of similar rope ?

A

12 cm

B

6 cm

C

3 cm

D

`1.5 cm`

Text Solution

Verified by Experts

The correct Answer is:
B
`Y = (FL )/(ADelta L )`
Breaking force `F prop A`
`therefore ( F _(R))/( F _(1)) = (A _(2))/( A _(1)) = (pi D _(2) ^(2))/( pi D _(1) ^(2)) ((D _(2))/( D _(1))) ^(2)`
`therefore (D _(2))/( D _(1)) = ((F _(2))/F_(1))^(1//2)= ((600)/(150))^(1//2) = (4) ^(1//2)`
`therefore D _(2) = D _(1) xx 2`
`therefore D _(2) = 3 xx 2 `
`therefore D _(2) = 6 cm`
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