Q 11-08-071JEE MainJEE Main 2022 (26 Jul, Shift 2)Easy
The area of cross section of the rope used to lift a load by a crane is $2.5\times10^{-4}\ \text{m}^2$. 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 $g = 10\ \text{m s}^{-2}$)
Answer: (A) $6.25\times10^{-4}\ \text{m}^2$
The maximum stress (breaking stress) is fixed, so the load is proportional to the area:
$$A' = 2.5\times10^{-4}\times\frac{25}{10} = 6.25\times10^{-4}\ \text{m}^2$$
Solution by Sreeraj P, M.Sc Physics