The area of cross section of the rope used to lift a load by a crane is $2 . 5 \times {10}^{- 4}{m}^{2}$ . The maximum lifting capacity of the crane is $10$ metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be
(take $g = 10{ms}^{- 2}$ )

Question

The area of cross section of the rope used to lift a load by a crane is

2 . 5 \times {10}^{- 4}{m}^{2}

. The maximum lifting capacity of the crane is

10

metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be
(take

g = 10{ms}^{- 2}

)

Quantrex Academy · Accepted Answer

Correct answer: A. 6 . 25 × 10 ^ - 4 m ^ 2

Since breaking stress (Maximum lifting capacity) is the property of material, so it will remain same.
Now, breaking stress $= \dfrac{Maximumliftingcapacity}{Areaofcrosssectionofrope}$
$⇒ \dfrac{10}{2 . 5 \times {10}^{- 4}} = \dfrac{25}{A}$
$A = 625 \times {10}^{- 6}$
$= 6 . 25 \times {10}^{- 4}{m}^{2}$

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