To analyze the gravitational pull on the surfaces of two planets with the same mass but different sizes, we need to consider the formula for gravitational acceleration at the surface of a planet, which is given by:
\[ g = \frac{GM}{R^2} \]
where:
- \( g \) is the gravitational acceleration,
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the planet,
- \( R \) is the radius of the planet.
Since both planets have the same mass \( M \), the key factor influencing the gravitational pull is the radius \( R \).
- For the smaller planet (which has a smaller radius), the value of \( R \) in the denominator will be smaller, resulting in a larger value of \( g \).
- For the larger planet (which has a larger radius), the value of \( R \) in the denominator will be larger, resulting in a smaller value of \( g \).
Thus, the objects would experience a greater gravitational pull on the smaller planet because the gravitational acceleration is inversely proportional to the square of the radius.
Therefore, the correct statement is:
The objects would experience a greater gravitational pull on the smaller planet.