Question

In figure. 1 below, a particle of mass m is initially at point A, a distance d from the center of one uniform sphere and distance 4d from the center of another identical uniform sphere, both of mass M>>m. State whether, if you moved the particle to point D, the following would be positive, negative, or zero and why: a) the change in the gravitational potential energy of the particle. b) the work done by the net gravitational force on the particle. c) the work done by your force that moves the particle. d) What are the answers if, instead, mass m was moved from point B to C? Kd d -d -d -d mo A B с D M м fig. 1

Answer 1

body of mass 'm' which is The gravitational potential energy of distance of es from another body at a of 'M is given by mass U = -GmM where G = 6.6738 10-" Ninh N.mt/kg ² is gravitational Constant. When the particle is at A, the potential energy of the particle is -GmM d GMM 40 -56mm 4d When it is at D, U = -GmM 4d GmM d -SGmM 4d At B, UB -GMM d GmM ad - 36mm 2d At C, Uc = - GmM ad GmM व - 36mm ad did not change (a) when moved from A to D, the particle's potential energy UA = Up - 5GmM → change in gravitational potential as We See ad is energy Zeyo =0.J AD (b) Since the change in energy is zero, the work done by the net forces zero. Implies the work done by net gravitational forces is also is WEG от (c) work done by your force is also zero. = OJ (d) Ug = Uc , So ΔΟ BC =OJ and here also the work done are zero. » WFG = WE =oJ