IIT JEE , AIEEE Forum - Physics , Mechanics

gopi_mith

The value of G can be determined experimentally using the famous CAVENDISH EXPERIMENT:
A bar AB is taken which is suspended from a rigid support by a fine wire. the bar has two small lead spheres attached at its ends. now two large lead spheres are brought close to the small ones by equal and opposite forces.
there is no net force on the bar, but a torque acts which is equal to F times the length of the bar, where F is the force of attraction between a big sphere and its neighbouring small sphere.
Due to this torque the suspended wire gets twisted till such time as the restoring torque of the wire equals the gravitational torque
if $ is the angle of the twist of the suspended wire, the restoring torque is proportinal to $ and is equal to T$ where T is the restoring couple per unit angle of twist.
T can be measured independently by applying a known torque and measuring the angle of twist.
the gravitational force between the spherical balls is the same as if their masses are concentrated at their CENTRES.
thus if d is the separation between the centres of the big and its neighbouring small sphere, with M and m as their masses, the gravitational force between the big sphere and its neighbouring small sphere is,
F=G(Mm)/d^2
if L is the length of the bar AB, then the torque arising out of F is FL.
At equilibrium,this is equal to the restoring torque.
Hence,
G(MmL)/d^2= T$.
Observation of $ thus enables one to calculate G from this equation.
this experiment was later refined and the accepted value of G is 6.67x10^-11 Nm^2kg^-2

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