In introductory physics laboratories, a typical Cavendish balance for measuring the gravitational constant G uses lead spheres of masses 1.79 kg and 16.9 g whose centers are separated by 5.49 cm. Calculate the gravitational force between these spheres, treating each as a point mass located at the center of the sphere. The value of the universal gravitational constant is 6.67259 × 10−11N · m2/kg2.

That is simply a matter of computing

G*M1*M2/R^2

They have told you what all the terms are. Do the calculation.

To calculate the gravitational force between the spheres, we can use the equation for gravitational force:

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

Where:
F is the gravitational force between the spheres.
G is the universal gravitational constant, whose value is given as 6.67259 × 10^-11 N · m^2/kg^2.
m1 and m2 are the masses of the spheres.
r is the distance between the centers of the spheres.

In this case, we have:
m1 = 1.79 kg
m2 = 16.9 g = 0.0169 kg (since 1 g = 0.001 kg)
r = 5.49 cm = 0.0549 m (since 1 cm = 0.01 m)

Plugging these values into the equation, we get:

F = (6.67259 × 10^-11 N · m^2/kg^2) * (1.79 kg) * (0.0169 kg) / (0.0549 m)^2

Calculating this expression will give us the desired gravitational force between the spheres.