3gravity at its surface is `g`. wat do u mean by this ???
an interstellar explorer discovers a remarkable planet made entirely of uniform compressible fluid of density Ï.the radius of the planet is `r` and the gravity at its surface is `g`. wats the pressure at the centre of the planet?
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13 Answers
1we have dP=-GMλxdx/R3
so we have P=P0+GMλ/2R
but P0=0
but we have g=GM/r2
thus we get λ as 3g/4πGr
solving it we get P
9rohan
we can find λ theoretically itself
its actually =Ï only!!
so i guess we need to represent P in terms of Ï,g,r and not use G
final ans= gÏr/2 is it correct b555 ?
9yes language is wrong it shud read as
acc due to gravity is g
1but celestine λ is not mentioned so you need to convert it in terms of given quantities
we get thus answer as g*(3g/4Ï€Gr)*r/2=3g2/8Ï€G
9rohan u can derive λ=Ï easily and moreover u r not supposed to give final ans in G as its unknown here !!!!
we know only g,Ï,r !!
1oops didnt see that p was already mentioned in problem
but one thing celes , G is a universal constant isnt it?
1pressure at any distance x from the centre is given by
dp(4pi x2)=-(4/3pix3)d*G*d*(4pix2)dr/r2
{i know its my fault for not using the edittor)
we basically have
dp=-4/3piGd2 rdr
integrating with proper limits gives us the presure at the centre as
GMd/2R =dgR/2
cheers!!
9yes it is universal constant but then its value isnt mentioned in prob
1well actually i didnt see that p was already mentioned in problem ... that is why i was going about that way ..