Editing Content :: Admin Scraper

Chapter

Content type

Position

Value

GRAVITATION 131 cases,a simplelawresultswhenyoudothat: (1) 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 variousregionsoftheshellhavecomponents along the line joining the point mass to the centre as well as along a direction Fig. 7.5 Three equal masses are placed at the three perpendicular to this line. The components perpendicular to this line cancel out when vertices of the ABC. A mass 2m is placed summing over all regions of the shell leaving at the centroid G. only a resultant force along the line joining Gm 2m  the point to the centre. The magnitude of FGA  ˆj this force works out to be as stated above. 1 (2) The force of attraction due to a hollow Gm 2m spherical shell of uniform density, on a FGB   i cos 30  j sin 30  point mass situated inside it is zero. 1 Qualitatively, we can again understand this Gm 2  ˆ  ˆ  result. Various regions of the spherical shell FGC  1 i cos 30  j sin 30  attract the point mass inside it in various directions. These forces cancel each other From the principle of superposition and the law of vector addition, the resultant gravitational completely. force FRon (2m) is F = F + F + F 7.4 THE GRAVITATIONAL CONSTANT R GA GB GC FR 2Gm j  2Gm 2 i cos30 jsin30  The value of the gravitational constant G entering the Universal law of gravitation can be  2Gm 2i cos 30  j sin 30 0 determinedexperimentallyandthiswasfirstdone Alternatively, one expects on the basis of by English scientist Henry Cavendish in 1798. symmetry that the resultant force ought to be The apparatus used by him is schematically zero. shown in Fig.7.6 (b) Now if the mass at vertex A is doubled then ⊳ For the gravitational force between an extended Fig. 7.6 Schematic drawing of Cavendish’s object(liketheearth)andapointmass,Eq.(7.5)isnot experiment. S 1nd S a2e large spheres directlyapplicable.Eachpointmassintheextended which are kept on either side (shown object will exert a force on the given point mass and shades) of the masses at A and B. When the big spheres are taken to the other side these force will not all be in the same direction. We of the masses (shown by dotted circles), havetoadduptheseforcesvectorially forallthepoint the bar AB rotates a little since the torque masses in the extended object to get the total force. reverses direction. The angle of rotation can This is easily done using calculus. For two special be measured experimentally. Reprint 2026-27