Yes because the earth will apply equle force and opposite to both object it means the both object will have same masses

Newton's Law of Gravitation:
Newton's law of gravitation states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, it can be represented as:

F = G * (m1 * m2) / r^2

Where:
- F is the force of attraction between the two bodies
- G is the gravitational constant
- m1 and m2 are the masses of the two bodies
- r is the distance between the centers of the two bodies

Equal Force on Two Bodies:
Let's consider two bodies, A and B, that are held near the Earth. The Earth exerts an equal force on both bodies. We can represent this as:

Force on body A = Force on body B

Using Newton's law of gravitation, we can represent the forces as:

G * (m1 * mEarth) / r^2 = G * (m2 * mEarth) / r^2

Here, mEarth represents the mass of the Earth. Since the distance between the bodies and the Earth is the same, we can cancel out the r^2 terms.

m1 * mEarth = m2 * mEarth

Proving Equal Masses:
To prove that the masses of bodies A and B are equal, we can cancel out the mEarth terms:

m1 = m2

Therefore, if the Earth exerts an equal force on two bodies held near it, their masses are equal.

Explanation:
According to Newton's law of gravitation, the force of attraction between two bodies is directly proportional to their masses. When the Earth exerts an equal force on two bodies, it means that the force of attraction experienced by both bodies is the same. By setting up the equation based on Newton's law of gravitation, we can see that the masses of the two bodies must be equal for the forces to be equal.

This implies that if the Earth exerts the same gravitational force on two bodies held near it, then their masses are equal. This conclusion is consistent with our understanding of gravity, as the force of gravity depends on the mass of an object. Therefore, if the forces are equal, the masses must also be equal.