The area of cross section of the rope used to lift a load by a crane is 2.5 × 10^–4 m². 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)

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$1 .67 \times 10^{- 4} m^{2}$

$1 \times 10^{- 4} m^{2}$

$10 \times 10^{- 4} m^{2}$

$6 .25 \times 10^{- 4} m^{2}$

answer is A.

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Detailed Solution

Since breaking stress (Maximum lifting capacity) is the property of material so it will remain same.

$breaking stress = \frac{Maximum lifting capacity}{Area of cross section of rope}$

$\begin{array}{l} \frac{10}{2 .5 \times 10^{- 4}} = \frac{25}{A} \\ A = 625 \times 10^{- 6} \\ = 6 .25 \times 10^{- 4} m^{2} \end{array}$

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