Lesson 4 of 11 · 6 min
The gravitational constant
NCERT §7.4
Two people standing a metre apart pull each other with less than a millionth of a newton. To measure G, Henry Cavendish in 1798 had to detect a force that small between lead spheres, in a sealed room, reading the result through a telescope.
The lesson in notes
In short
G was first measured by Henry Cavendish in 1798, with a torsion balance.
A light bar AB with a small lead sphere at each end hangs from a fine wire. Two large lead spheres are placed near the small ones, on opposite sides.
The two attractions are equal and opposite, so there is no net force on the bar, only a torque F × L that twists the wire.
The wire twists until its restoring torque τθ balances the gravitational torque: G M m L / d² = τθ, where τ is the restoring torque per unit twist, found separately.
Measuring θ gives G. The accepted value is G = 6.67 × 10⁻¹¹ N m² kg⁻², the same everywhere, which is why it is called universal.
G is tiny: two 1 kg masses 1 m apart attract with only 6.67 × 10⁻¹¹ N, which is why gravity between everyday objects goes unnoticed.