Final answer:
The gravitational acceleration on this hypothetical planet would be four times that of Earth's because the formula for gravitational acceleration is inversely proportional to the square of the radius.
Step-by-step explanation:
If scientists discover a planet with exactly the same mass as Earth's but a radius half as small as Earth's, the gravitational acceleration on the surface of this planet would be different. The gravitational acceleration is given by the formula G * (mass of the planet) / (radius of the planet)^2. Since the mass of the planet is the same as Earth's, but the radius is half, we would square 1/2 to get 1/4. Thus, the gravitational acceleration on this planet would be four times that of Earth's, because while the mass remains the same, the effect of the smaller radius is squared in the denominator, making the overall acceleration larger.
For example, Earth's gravitational acceleration is approximately 9.81 m/s². On a planet with half Earth's radius, the gravitational acceleration would be 4 times larger, so it would be about 39.24 m/s².