B

Step 1: Understand the Setup
Given that the mirror is at the center of curvature of the spherical screen, it will reflect light in such a way that the path traced by the light spot on the screen will depend on the angular velocity of the mirror.

Step 2: Calculate Angular Velocity
The angular velocity \( \omega \) is given as 0.5 revolutions per second. To convert this to radians per second, we can use the fact that one revolution is equal to \( 2\pi \) radians:
\[ \omega = 0.5 \text{ rev/s} \times 2\pi \text{ rad/rev} = \pi ext{ rad/s} \]

Step 3: Determine the Velocity of the Light Spot
As the mirror revolves, the spot of light moves along the circular path on the spherical screen. The radius of this path is equal to the radius of the sphere, which is given as 10 meters.

The linear velocity \( v \) of the light spot can be calculated using the formula:
\[ v = r \cdot \omega \]
where \( r \) is the radius of the circle traced by the light spot, and \( \omega \) is the angular velocity.

Substituting the values:
\[ v = 10 ext{ m} \cdot \pi ext{ rad/s} = 10\pi ext{ m/s} \approx 31.42 ext{ m/s}
\]

Step 4: Conclusion
The velocity of the light spot moving along the spherical screen is approximately 31.42 m/s.