Observation of θ thus enables one to

Observation of θ thus enables one to calculate G from this equation. Since Cavendish’s experiment, the measurement of G has been refined and the currently accepted value is G = . × - N m /kg ( . ) . ACCELERATION DUE TO GRAVITY OF THE EARTH The earth can be imagined to be a sphere made of a large number of concentric spherical shells with the smallest one at the centre and the largest one at its surface. A point outside the earth is obviously outside all the shells. Thus, all the shells exert a gravitational force at the point outside just as if their masses are concentrated at their common centre according to the result stated in section . . The total mass of all the shells combined is just the mass of the earth. Hence, at a point outside the earth, the gravitational force is just as if its entire mass of the earth is concentrated at its centre. For a point inside the earth, the situation is different. This is illustrated in Fig. . . Fig. . The mass m is in a mine located at a depth d below the surface of the Earth of mass M E and radius R E . We treat the Earth to be spherically symmetric. Again consider the earth to be made up of concentric shells as before and a point mass m situated at a distance r from the centre. The point P lies outside the sphere of radius r . For the shells of radius greater than r , the point P lies inside. Hence according to result stated in the last section, they exert no gravitational force on mass m kept at P. The shells with radius ≤ r make up a sphere of radius r for which the point P lies on the surface. This smaller sphere therefore exerts a force on a mass m at P as if its mass M r is concentrated at the centre. Thus the force on the mass m at P has a magnitude Gm M ( . ) We assume that the entire earth is of uniform density and hence its mass is ρ where M E is the mass of the earth R E is its radius