Answer :
Final answer:
The applied stress on a steel wire with a diameter of 2 mm under a load of 25 kg (245 N) is calculated to be 78.04 MPa. Therefore, none of the options are correct.
Explanation:
The applied stress in a steel wire under load within the elastic range. Stress ( estsigma ) is defined as the force (F) divided by the area (A) over which the force is uniformly distributed. The area can be calculated using the formula A = ( pi /4) d^2 , where d is the diameter of the wire. The force can be converted from kilograms to newtons by multiplying by the acceleration due to gravity, which is approximately 9.8 m/s ^2 .
Using these definitions, the stress on a wire with a diameter of 2 mm (0.002 m) and a load of 25 kg (245 N) can be calculated as follows: Determine the cross-sectional area: A = (pi/4) * d ^2 = (3.14/4) * (0.002 m) ^2 = 3.14 * 10^{-6} m ^2 Convert the load from kg to N (1 kg = 9.8 N): F = 25 kg * 9.8 m/s ^2 = 245 N
Calculate stress ( estsigma ): estsigma = F/A = 245 N / (3.14 * 10^{-6} m ^2 ) = 78,038,216.56 Pa or 78.04 MPa. However, none of the given options, a) 159 MPa, b) 195 MPa, c) 231 MPa, or d) 278 MPa, match the calculated stress. Therefore, there might be an error either in the question or the options provided.
