According to Newton's law of universal gravitation, the force of gravitation between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:

$$F = (Gm_1m_2)/r^2$$

where,

F is the force of gravitation

G is the gravitational constant (approximately 6.674 × 10^-11 N·m^2/kg^2)

m1 and m2 are the masses of the two objects

r is the distance between the centers of the two objects

If the distance between the objects increases by an amount of 10, then the new distance between them would be 10r. By substituting this new distance in the formula, we can determine the new force of gravitation:

$$F' = (Gm_1m_2)/(10r)^2$$

Simplifying the equation, we can rewrite it as:

$$F' = (Gm_1m_2)/(100r^2)$$

By comparing this equation with the original expression for F, we can see that the new force of gravitation is reduced by a factor of 100 due to the increased distance. In other words, the force becomes 1/100th of its original strength:

$$F' = F/100$$

Therefore, if the distance between the two objects were to increase by 10 times, the force of gravitation between them would reduce to 1/100th of its original value.