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how can do the measurement of gravitational constant G
The gravitational constant G is a small quantity and its measurement needs very sensitive arrangement. The first important successful measurement of this quantity was made by Cavendish in 1736 about 71 years after the saw was formulated.
In this method, two small balls of equal mass are attached at the two ends of a light rod to form a dumb bell. The rod is suspended vertically by a fine quartz wire. Two large spheres of equal mass are placed near the smaller spheres in such a way that all the four spheres are on a horizontal circle. The centre of the circle is at the middle point of the rod.
Two larger spheres lie on the opposite sides of the smaller balls at equal distance. A small plane mirror is attached to the vertical wire. A light beam, incident on the mirror, falls on a scale after reflection. If the wire rotates by an angle θ, the reflected beam rotates by 2θ and the spot on the scale moves. By measuring this movement of the spot on the scale and the distance between the mirror and the scale, the angle of deviation can be calculated. When the heavy balls are placed close to the small balls, a torque acts on the dumb ball to rotate it. AS the dumb bell rotates, the suspension wire gets twisted and produces a torque on the dumb bell in opposite direction. This torque is proportional to the angle rotated. The dumb bell stays in equilibrium where the two torques have equal magnitude.
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