How can we measure gravitational constant in the lab?

The gravitational constant can be measured in the lab using a torsion balance, as in the Cavendish experiment.

The Cavendish experiment, conducted by Henry Cavendish in 1798, is the most common method used to measure the gravitational constant, often denoted as 'G'. The experiment involves a torsion balance, a horizontal bar suspended from a thin wire, with small lead spheres attached to each end. Larger lead spheres are placed close to the smaller ones, and the gravitational attraction between them causes the bar to twist, twisting the wire. The amount of twist is proportional to the gravitational force between the spheres.

The gravitational force can be calculated using Newton's law of universal gravitation, which states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. This force is given by the equation F = G(m1m2)/r², where F is the gravitational force, m1 and m2 are the masses of the particles, r is the distance between the centres of the two particles, and G is the gravitational constant.

By measuring the amount of twist in the wire, the distance between the spheres, and the masses of the spheres, the gravitational constant G can be calculated. This is a very delicate experiment and requires careful control of environmental factors such as temperature and air currents, as these can affect the results.

The Cavendish experiment is a classic physics experiment and is often replicated in physics labs to measure the gravitational constant. However, it's worth noting that the value of G is one of the least accurately known of the fundamental constants, due to the difficulty in measuring it accurately. Despite this, the Cavendish experiment provides a good approximation and is a fascinating demonstration of the principles of gravitational attraction.