86.2 Gravitational force of a uniform sphere on a particle Exercise 2: a particle of mass m is placed on the axis of a circular ring of mass M and radius Find the gravitational force exerted by the ring on the particle located a distance from the center of the ring. R n 86.2 Gravitational force of a uniform sphere on a particle Solution: dm dF=dF cosa M dF dF mdM dF=g Gm dM F dF cos a (R2+x2)√R2+x MmX (R2+x 3/2 F=-F i9 §6.2 Gravitational force of a uniform sphere on a particle Exercise 2: a particle of mass m is placed on the axis of a circular ring of mass M and radius R. Find the gravitational force exerted by the ring on the particle located a distance from the center of the ring. O x m M R §6.2 Gravitational force of a uniform sphere on a particle Solution: x O M m R F r d α dM dFx = dF cosα 2 d d r m M F = G 2 2 3 2 0 2 2 2 2 ( ) ( ) d d cos R x GmMx R x x R x Gm M F F M x + = + + = = ∫ ∫ α F F i x ˆ = − r F r d