triangle ABC. (a) What is the force acting on a mass m placed at the centroid G of the triangle? (b) What is the force if the mass at the vertex A is doubled ? Take AG = BG = CG = m (see Fig.
. ) Answer (a) The angle between GC and the positive x -axis is ° and so is the angle between GB and the negative x -axis. The individual forces in vector notation are Fig. .
Gravitational force on m due to m is along r where the vector r is ( r – r ). O cases, a simple law results when you do that : ( ) The force of attraction between a hollow spherical shell of uniform density and a point mass situated outside is just as if the entire mass of the shell is concentrated at the centre of the shell. Qualitatively this can be understood as follows: Gravitational forces caused by the various regions of the shell have components along the line joining the point mass to the centre as well as along a direction prependicular to this line. The components prependicular to this line cancel out when summing over all regions of the shell leaving only a resultant force along the line joining the point to the centre.
The magnitude of this force works out to be as stated above. ( ) The force of attraction due to a hollow spherical shell of uniform density, on a point mass situated inside it is zero. Qualitatively, we can again understand this result. Various regions of the spherical shell attract the point mass inside it in various directions.
These forces cancel each other completely. . THE GRAVITATIONAL CONSTANT The value of the gravitational constant G entering the Universal law of gravitation can be determined experimentally and this was first done by English scientist Henry Cavendish in . The apparatus used by him is schematically shown in Fig.
. Fig. . Schematic drawing of Cavendish’s experiment.
S and S are large spheres which are kept on either