Question

The area of cross section of the rope used to lift a load by a crane is $2.5 × 10^{–4}$ $m^2$. 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

• A. $6.25 × 10^{–4} \;m^2$
• B. $10 × 10^{–4} \;m^2$
• C. $1 × 10^{–4}\; m^2$
• D. $1.67 × 10^{–4}\; m^2$

Answer 1

Answer: (A)

$6.25 × 10^{–4} \;m^2$

Answer 2

area of cross section of the rope :

= $\frac{25}{10} \times 2.5 \times 10 ^{-4} \;\bigg[ A_2 = \frac{W_2}{W_1} A_1\bigg]$

= $6.25 \times 10 ^{-4}\; m^2$