#### Answer

(a) The magnitude of the gravitational force of attraction that each ball exerts on the other is $6.67\times 10^{-9}~N$.
(b) The ratio of this gravitational force to the weight of the 100-gram ball is $6.81\times 10^{-9}$.

#### Work Step by Step

(a) We can find the magnitude of the gravitational force of attraction that each ball exerts on the other.
$F = \frac{G~M_1~M_2}{R^2}$
$F = \frac{(6.67\times 10^{-11}~m^3/kg~s^2)(10~kg)(0.10~kg)}{(0.10~m)^2}$
$F = 6.67\times 10^{-9}~N$
The magnitude of the gravitational force of attraction that each ball exerts on the other is $6.67\times 10^{-9}~N$
(b) We can find the ratio of this gravitational force to the weight of the 100-gram ball.
$\frac{F}{M_2~g} = \frac{6.67\times 10^{-9}~N}{(0.10~kg)(9.80~m/s^2)} = 6.81\times 10^{-9}$
The ratio of this gravitational force to the weight of the 100-gram ball is $6.81\times 10^{-9}$.