`implies` The value of the gravitational constant G can be determined experimentally and this was first done by Cavendish in 1798. The apparatus used is schematically shown in figure.
`implies` The bar AB has two small lead spheres attached at its ends. The bar is suspended from a rigid support by a fine wire.
`implies` Two large lead spheres are brought close to the small ones but on opposite sides. The big spheres attract the nearby small one by equal and opposite force. There is no net force on the bar but only a torque which is clearly equal to F times the length of the bar, where F is the force of attraction between a big sphere and small sphere. As a result bar rotates about OM (wire). So, wire gets twisted till such time as the restoring torque of the wire equals the gravitational torque.
`implies` In this position sphere A and B remains stable and angle of twist `theta` can be measured.
`implies` In this position of large sphere `S_1 and S_2` or `S._1 and S._2` . is on to the line perpendicular line AB.
`implies` Suppose, M and m are mass of large and small sphere respectively. In equilibrium the distance between their centre `= AS_(1) - BS_(2) = d` and in this position angle of twist is and torsion constant k and length of rod AB = l.
`implies` Gravitational force on sphere A and B,
`F = (GMm)/d^2`
The restoring torque acting on sphere A and B,
`tau = FL`
`tau = (GMm)/d^2 L " "...(1)`
and restoring torqure produced in wire ,
`tau. = k theta " "...(2)`
`:.` For equilibrium` tau = tau.`
`(GMm)/d^2L= k theta`
`:. G = (k thetad^2)/(MmL)" " ....(3)`
`implies` Here, value of `theta` obtain by lamp and scale method and int `tau = k theta` if value of `tau` is known then angle of twist (due to torque t.) will be determined and hence `k = tau / theta` be calculated.
`:.` In equation (3), by putting the value of right terms, value of G can be determined.
`implies` By this experiment Cavendish found the value of `G = 6.67 xx 10^(-11) (Nm^2)/(kg^2)` and it is currently accepted.
`implies` Dimensional formula of G is `M^(-1) L^(3) T^(-2)`.
