the radius of the differential disc element that you consider on moving a distance 'x' from the apex is proportional to x^2. hence its mass is also proportional to x^2...
SIR PLEASE SOLVE THE PROBLEM GIVEN BELOW PLEASE!! A child of mass m sits in a swing of negligible mass suspended by a rope of length l. Assume that the dimensions of the child are negligible compared with 1. His father pulls the child back until the rope makes an angle of one radian with vertical, then pushes with a force F=mg along the arc of the circle releasing at the vertical : a) How high up will the swing go? b) How long did the father push?
(l^n-(l-2)^n)^1/n
ReplyDeletespeed thrills..and kills!
ReplyDeletego a bit easy man!
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ReplyDeletei know bhaiya.
ReplyDeletei know misfired.
is it l-(l^n-(l/2)^n)^1/n??
na...yaar put n=0 for a uniform rod and check..
ReplyDeletebhaiya shudn't it b n=1 fr unifrom rod??
ReplyDeletena..
ReplyDeletelinear mass density is constant and hence proportional to x^0..
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ReplyDeleteThis comment has been removed by the author.
ReplyDeletewhat happened
ReplyDeletey'd u remove the post
is my answwr correct
haan yaar..teri post rremove kar di taki sab answer na dekh lein!
ReplyDeletehey kapil..use the result to find the COM of a solid and hollow cone..
ReplyDeleteIs the answer.
ReplyDeleteCOM=L/(n+2) from end B.
haan yaar
ReplyDeletefor a solid cone,
density d is proportional to (r^2) and x/H=r/R
so d is proportional to x^2
so, com is H/4 from bottom
similarly for hollow cone
we get d proportional to r[sqrt(x^2+r^2)]/x
put x/H=r/R to get d proportional to x
and so com is H/3 from bottom
really gud ....
L/n+2
ReplyDeletend ye method of finding fr cone .. bhi mast h !! :)
because then you don't have to integrate
ReplyDeleteL/n+2.
ReplyDeleteAT KAPIL ,great method for finding com for cone
Can somebody explain me the post from kapil.
ReplyDeletethat how is d proportional to them in both the cases.
Thanx
the radius of the differential disc element that you consider on moving a distance 'x' from the apex is proportional to x^2.
ReplyDeletehence its mass is also proportional to x^2...
similarly formulate for a hollow cone!
yess l/n+2
ReplyDeletewe did this type of question in class( there n was 1). we also derived area of circle= pi r^2 ....i understood the importance of integration that day
but my answer is coming out to be L*(n+1)/(n+2)
ReplyDeleteplease tell me where am i wrong.
Vijay,you got the distance from A .For distance from B , subtract your answer from L.
ReplyDeleteSIR PLEASE SOLVE THE PROBLEM GIVEN BELOW PLEASE!! A child of mass m sits in a swing of negligible mass suspended by a rope of length l. Assume that the dimensions of the child are negligible compared with 1.
ReplyDeleteHis father pulls the child back until the rope makes an angle of one radian with vertical, then pushes with a force F=mg along the arc of the circle releasing at the vertical :
a) How high up will the swing go?
b) How long did the father push?
ans:(a) theta=63degree above horizon (b) t=1.52(l/g)^1/2