Question

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

विकल्प

• 6.25 × 10^-4m²

• 10 × 10^-4m²

• 1 × 10^-4m²

• 1.67 × 10^-4m²

Answer 1

The area of the cross-section of the rope used to lift a load by a crane is 2.5 × 10^-4m². 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 the cross-section of the rope should be 6.25 × 10^-4m².

Explanation:

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

breaking stress = `("Maximum lifting capacity")/("Area of cross-section of rope")`

⇒ `10/(2.5 xx 10^-4) = 25/A`

⇒ A = `(25 xx 2.5 xx 10^-4)/10 = 625 xx 10^-6 = 6.25 xx 10^-4 "m"^2`