Question

Cavendish experiment to measure \[G\] uses the concept of-
(A). Torque
(B). Force
(C). Force-Torque Equilibrium
(D). None of these

Answer 1

Hint: Cavendish used an apparatus for his experiment in determining the magnitude of gravitational forces between two bodies which later became the basis for calculating gravitational constant. He used the torsion balance with two lead spheres of different sizes.

Complete answer:
Henry Cavendish, an English scientist performed an experiment to measure the magnitude of gravitational force between two bodies. This experiment later became the basis for calculating the value of \[G\].
The main aim of his experiment was to use Newton’s Law of universal gravitation which states that any two bodies in the universe attract each other with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
\[F\propto \dfrac{{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\]
Here, \[{{m}_{1}}\,and\,{{m}_{2}}\] are the masses of the two bodies respectively.
\[r\] is the distance between them.
For his experiment, Cavendish used a rod connected to a torsion balance.
A torsion balance is an apparatus in which a wooden rod is freely suspended from a thin wire with two small masses suspended at its ends. The wire undergoes torsion due to the torque applied at its ends as different masses are affected differently by the gravitational force of earth.
It is based on the principle that a wire resists torsion with a force that is directly proportional to the stress in it.
Cavendish used two lead spheres of \[0.73\text{ }kg\] hung from each end. Another large lead sphere of mass \[158kg\] was placed at each end of the torsion balance. The gravitational forces acting between the smaller and larger sphere lead the rod to twist along a graduated scale but this torsion was counteracted by the restoring force due to stress and this caused the rod to move like a pendulum.
Therefore, the calculation of \[G\] was done using torsion balance which uses the concept of force-torque equilibrium.

So the correct option is (C).

Note:
Torsion Balance was invented by John Mitchell who was an English geologist, astronomer and a colleague of Cavendish. He also used this apparatus to calculate Earth’s mean density. The value of gravitation constant is\[G=6.67\times {{10}^{-11}}N{{m}^{2}}k{{g}^{-1}}\]. Cavendish did the experiment in a sealed room as even the smallest disturbances could give wrong readings.