3hey ram i asked akand for the type of the sphere. if it is an insulating sphere then the field inside the sphere will vary and correspondingly it is a pbm similar to our problem
A body of superdense material with mass twice the mass of earth butsize very small compared oto the size of earth starts from rest from h<<R above the earth's surface. It reaches earth in time
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3ram i thought the 2m mass will hit the earth . there will be collision between the two bodies . and i assumed that e wiil one for the collision
1AND U ASSUMED DAT .................................. I CLDN GET U AFTER DAT......
31K.. K........ DATS A NICE CLUE 2 GET........ BUT AKANDS BUSY WIT INSTNT CHAT........
11596 Views (till now)...................158 posts (till now).................5 Users..............1 Topic!
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And it ain't over yet!
11K. What's the final solution to this problem? First I thought it was a simple problem and now it's become one of the longest topics ever.(mainly because half the posts there are bullshit!)
1hii gang !!!!
r we getin any prize for making it the longest thread ever(:D)
for others i will try to summarise our discussion(dat is topic related discussion)
1simply use centre of mass principle............
answer is √[2h/3g]..................
1hey dat was nt ma question.......... let me solve it out.... wt fr a while.......
1but sankar has d solution as √2h/3g.........
he too doesnt knew d way of solvin...........
11Tomorrow is the 1week aniversary of this thread. Prizes to all the participants in this thread (except kartik) will be awarded by Nishant bhaiyyah at 4:02pm. [4]
1Yaar...this question is quite easy...
(h and x are exaggerated)
Using Law of gravitation and centre of mass concept [M1a1 = M2a2],
we get
acc of earth = 2g
acc of mass = g
Now, we see that both the mass and the earth will move towards their common center of mass (at 2R/3 from centre of earth)
that means the earth will move towards the mass.
Suppose at time t, the earth moves x.
thus, the mass will move (h - x) in same time t.
x = 1/2 (2g) t2........................................... (1)
=> t =√x/g
also,
h - x = 1/2 (g) t2
h - x = 1/2 (g) x/g
h = 3/2 (x)
=> x = 2/3 h
putting in (1), we get
t = √2h/3g
1h is negligible doesn't mean that the mass is already on the surface of earth....
it means that g doesn't change wid height...
11Thanx Shreyan. [4] You will receive an award tomorrow as well[9] cos u have posted one of the more useful replies in this thread [3]. Thanx again [1]
1hey its not that much difficult!
we must consider the center of mass!
here centre of mass with respect to earth= (2m*h+0)/(m+2m)
which gives= 2h/3
so the actual distance to be covered by the body = h-(2h/3)
=h/3!
so as h<<r so
g remains constant!
s=ut+1/2at(2)
h/3=0+1/2gt2
which gives time to reach as t2=2h/3g !
ok....!
11If you're getting this considering earth as a point mass then think again. Earth is not to be considered as a point mass.
1ya as the question suggest that the body is very small in sixe as compared to earth so considering both is not wrong!!
1waah....after so many days.......we hav got an answer.......im so happy