Question

The minimum diameter of a mass less brass rod ,if it is to support a 400N load without exceeding its elastic limit is 1mm. the elastic limit of brass is---​

Answer 1

minimum diameter of brass rod is 1.16 mm

Q -> The minimum diameter of a mass less brass rod ,if it is to support a 400N load without exceeding its elastic limit is 1mm. the elastic limit of brass is 379 MPa.

we have to find minimum diameter of brass rod. cross sectional area is directly proportional to square of its diameter. [i.e., A = πD²/4 ] hence, to get minimum diameter, we have to find out minimum cross sectional area.

we assume that the force F = 400N brings us to the elastic limit.

so, stress = F/A

⇒379MPa = 400/A

⇒379 × 10⁶ = 400/A

⇒A = 400/379 × 10¯⁶ m²

⇒πD²/4 = 400/379 × 10¯⁶ m²

⇒D² = (4 × 400/379 × π) × 10¯⁶ m²

⇒D² = 1.344 × 10¯⁶ m²

⇒D = 1.16 mm

therefore, minimum diameter of brass rod is 1.16 mm