To determine the degree of curvature for a railway curve, we need to understand what the degree of curvature represents. The degree of curvature in railway engineering is defined as the angle subtended at the center of a circular curve by a 30-meter arc. This relationship is essential for computing the degree of curvature when the radius is known.

The formula to calculate the degree of curvature (D) is:

D = \frac{360}{2\pi R}\times \text{arc length}

In railway standards, the arc length is typically set at 30 meters. Therefore, the formula becomes:

D = \frac{360}{2\pi R} \times 30

Given:

• Radius, R = 875 \, \text{m}

Substituting these values into the formula, we get:

D = \frac{360 \times 30}{2\pi \times 875}

Calculate the degree of curvature:

D = \frac{10800}{2\pi \times 875}

D = \frac{10800}{5495.54}

D \approx 1.965 \approx 2^\circ

Therefore, the degree of curvature for a railway curve with a radius of 875 meters is approximately 2°.

Conclusion: The correct answer is 2^\circ, matching the given correct answer option.