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.$.........\times 10^{-4} \,m ^{2}$ (take $g =10\, ms ^{-2}$ )
JEE MAIN 2022, Medium
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Since breaking stress (Maximum lifting capacity) is the property of material so it will remain same. breaking stress $=\frac{\text { Maximum lifting capacity }}{\text { Area of cross section of rope }}$ $\frac{10}{2.5 \times 10^{-4}}=\frac{25}{ A }$
$A =625 \times 10^{-6}$
$=6.25 \times 10^{-4} m ^{2}$
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