Final answer:
The magnitude of the net gravitational force on mass m2 is calculated by finding the difference between the gravitational forces exerted by m1 and m3 on m2. After computations following Newton's law of gravitation, the net force on m2 is found to be 2.22 × 10^-11 N, directed towards m3.
Step-by-step explanation:
To calculate the magnitude of the net gravitational force on mass m2 (3 kg), we must consider the gravitational forces exerted on it by both m1 (1 kg) and m3 (6 kg). According to Newton's law of gravitation, the force between two masses is given by F = G * (m1 * m2) / r^2, where G is the gravitational constant (6.674 × 10-11 N·m²/kg²), m1 and m2 are the masses, and r is the distance between the centers of the two masses.
The force between m1 and m2 is:
F1 = G * (m1 * m2) / r1^2 = (6.674 × 10-11 N·m²/kg²) * (1 kg * 3 kg) / (3 m)^2 = 2.22 × 10-11 N
The force between m2 and m3 is:
F2 = G * (m2 * m3) / r2^2 = (6.674 × 10-11 N·m²/kg²) * (3 kg * 6 kg) / (3 m)^2 = 4.44 × 10-11 N
Because m3 has a larger mass than m1, the force F2 is greater than F1, thus the net gravitational force on m2 will be towards m3. The net force is the difference between F2 and F1 because they are in opposite directions:
Net Force = F2 - F1 = (4.44 - 2.22) × 10-11 N = 2.22 × 10-11 N
Therefore, the correct answer to the magnitude of the net gravitational force on m2 is b) 2.22 x 10-11 N.