stat1;if the atmospheree air suddenly condenses n form a thin layer on the surface of earththe duration of day ll increase
stat2;moment of inertia of earth ll increase n thus angular speed ll decrease
1Bhaiyya thats wat I said in #5
I marked C becoz there is no e, like Amit said
1@Kalyan
We are including the mass of the atmosphere as well.
Moment of inertia = 2/5 MR2 {as earth is considered to be a solid sphere}
When the atmosphere condenses and forms a layer on the earth,
the total mass increases as well as its radius increases.
Hence, its moment of inertia increases.
1THe answer is D statement two is correct that if mass of earth will increase then moment of inertia will increase thus decreasing the angular speed, but statement one is wrong, hence option d
62I dont understand any of these logics...
I think you have all got it wrong.. or may be i havent read everything very closely..
Seee what is happening is that the earth in itself has no change in MI..
Lets look at the atmosphere....
any particles' inertia is dmr2
now r is reduced so inertia decreases...
So the inertia becomes less... I think that is the right way.
1I funniest part is i thought was that the answer shud be e- both statements are wrong, but since e was not given i said it is d
1Ya it is actly supposed to be none as I decreases 4 sure.
And to maintain a constant torque, ω increases, so the length of the day decreases.[7][7]
1@bhaiya...
v will not consider atmosphere while calculating d moment of inertia of earth... earth is taken as a solid sphere (where atmosphere covers it completely as a gaseous layer above it...)... so initially v don't consider atmosphere either for mass or for radius...
later when atmosphere condenses and forms a layer over d earth surface, it's weight is considered as it is solidified... so d net mass increases and also as it forms a layer above earth's surface, d radius also increases to a very small extent... which implies moment of inertia increases... hence angular speed decreases...
anything wrong in dis explanation... plz let me know...!!!
1Arrey but the atmosphere is always there. It rotates along with Earth.
So how can V leave it[7][7]
This is wat I have been saying from the beginning.
1So how can we take the mass of atmosphere insluded in the initial mass[7][7]
V cant take that just because answer aa raha hai............
Theek hai U may be right........
But wats the logic behind it[7]
1yaar.... in first condition atmosphere is a gaseous layer... which is not present in a fixed dimension... juzz lyk electron cloud around nucleus... whereas in second condition, atmosphere condenses, so it converts into either solid or liquid... wid a definite shape n weight... so dis tym v have to consider it...
(d reason y we neglect atmosphere in initial condition is similar to d reason y we consider only protons and neutrons to define atomic mass of an atom... while v neglect electrons as their mass is neglegible... similarly here mass of atmosphere is almost neglegible when compared wid d mass of solid earth)
1Even in case of atoms we consider the radius as the radius of the the complete atom including the electrons, we just leave out the mass becoz it is negligible.And its the same thing here, only that mass is not negligible.[5]
1Even in case of atoms we consider the radius as the radius of the the complete atom including the electrons, we just leave out the mass becoz it is negligible.And its the same thing here, only that mass is not negligible.[5]
62Mak I understand what you are trying to say.. but then I think that the atmosphere is not fully free!
Anyways the main point here has been discussed... It depends on your asumption about the atmosphere.. if you want to put it that way :)
1So, what is the final conclusion of this question??
I"m very much confused.
1hey the examiner has changed the ans .they have accepted c as crrct ans
1d question must be deleted... if statement 2 is false, it implies dat statement 1 is also false... how come d ans is C then...!!?
well, i got to learn a new point here, while considering d radius, v even take atmosphere into account... hmmm...!!!
not fully convinced though, but i wanna avoid this thought atleast for jee sake... so no more queries from me regarding this...!!!
1see the explaination provided
the atmosphere is rotating along wid the earth.when particle of atmosphere form part of solid earth,moment of inertia wud decrease.for conservation of angular momentum angular velocity wud increse n thus t wud decrease
1But if U C...
I is proportional to r2
So if r decreases I is supposed to decrease
So st2 is supposed to b wrong [337]
So if thats wrong it is supposed to be c..[7][7]
1the examiner might b a guy lyk me...!!! [3]
well, since d centripetal force is constant... i.e., d gravitational force... so it'll b somehow related to d product of moment of inertia(I) and angular speed(ω) rite... so this implies, I is inversely proportional to ω....
not sure though...!!!
1yeahhh...
y will it increase...??? it has to decrease rite...!!! [12]
1The answer will be A.
When the atmosphere condenses to form a layer around the earth, its radius increases.
Thus, the moment of inertia increases.
Since, the torque on the earth is constant. The angular velocity decreases.
As a result, the time taken for rotation increases increasing the duration of the day.
Hence, both statement-1 and 2 are correct and statement-2 is the correct explanation of statement-1.
Please tell me If I'm wrong in anyway.
ALL THE BEST
1@ragadeepika... here it's forming a layer on d surface of d earth... so radius will decrease, consequently d moment of inertia too...!!!
1I'm not able to get you.
Initially, the radius of earth be R.(say)
If a layer is formed on the earth with some thickness say x, then the radius of the whole sphere considering is R+x, which means it has increased.
richa and scorpion,
Can you please explain me why the radius will decrease.