Question

3. A particle of mass 1 kg is dropped into a hole drilled straight through Earth (not through the center). The shortest distance between the hole and the center of Earth is d. Neglecting rotational effects and assume Earth has uniform density. (1) If air resistance is negligible, solve the equation of motion to obtain the displacement of the particle as a function of time.

Answer 1

Sappose & is the posihm bf the panhicle in the tunnel AB attraction On it is due at instant The to The sphere of radiun oa, amd is dinected to ward 0, tho centre o sphere , The mas of this inner sphore on the parhele (of mam m) is F G(3)Pm(og) .If OP is Tthe component 3)TTP (og) and its attrochon drawn perpendicular to the tunnel FCos ZOg P- G() TAm (SP) of this force along P is Thus Componemt causen motion of m in the tunnel As an mooth this latter han been takem the tunnel combonent doen not affect the mohon along AB CAusing frichon The achve component is popartionas to the distamce of the barh cle from P dinected toeoands P. f Pg x the parhcle will be every where af motion t am d the eduaton -4) TT G Pmx writng wfar s) r GP the eduahon reduces Wha'ch is asell knoion edn Par SH.M

To solve, Let) A Sin kt puthng % +W2x=0 or, - AK2+ wA = o N4-TG1t SO, A Sin A Sinwt