Question

In introductory physics laboratories, a typical Cavendish balance for measuring the gravitational constant G uses lead spheres of masses 1.51 kg and 6.5 g whose centers are separated by 3.42 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^−11 N · m²/kg².

a) 2.87 × 10^−8 N
b) 2.03 × 10^−8 N
c) 4.67 × 10^−11 N
d) 5.69 × 10^−11 N

Answer 1

The gravitational force between two lead spheres in a Cavendish balance can be found using Newton's law of universal gravitation. With the provided mass and distance values, and the universal gravitational constant, the force is calculated to be approximately 2.03 × 10⁻⁸N.

Step-by-step explanation:

To calculate the gravitational force between two lead spheres in a Cavendish balance experiment, we use Newton's law of universal gravitation, stated in the formula F = Gm₁m₂/r², where F is the gravitational force, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers. Plugging in the given values, G = 6.67259 × 10⁻¹¹ N · m²/kg², m₁ = 1.51 kg, m₂ = 6.5 g (which is 6.5 × 10⁻³ kg to convert into kilograms), and r = 3.42 cm (which is 0.0342 m to convert into meters), we obtain the following:

F = (6.67259 × 10⁻¹¹ N · m²/kg²) × (1.51 kg) × (6.5 × 10⁻³ kg) / (0.0342 m)²

By performing the calculation, we find that F equals approximately 2.03 × 10⁻⁸ N, which corresponds to option (b) in the original question.