IIT JEE , AIEEE Forum - Physics , Mechanics

Conjurer

A good question

Conjurer

BUMP!

jinu.coolboy

Please write the question more clearly.

Conjurer

Click on the picture and save it/open it.

anandghegde

source of the question?

Conjurer

Get the paper from www.aiceonline.in

ganesha1991

which question ............i cudn't find that question
it wud be better if u post it here bro

rohith291991

*edited*

nishantsingh89

is the answer a) 2L/3V

velocity will not remain constant throughout as its a case of variable mass system, nd if you notice tht angular momentum will be conserved about lowest most point, as net torque is zero at this position,
, now as question states neglecting, rolling resistance, etc, so no dissipative forces acting on system so energy of system must be conserved

the lowest most point of roll is point of pure rotation , so total energy can be given by( question also says to neglect PE of system)
E= 1/2 * I*w^2 where I is MI about the point of pure rotation

now,

initial energy = 1/2 * 3/2 * M*R^2*w^2 = 3/4 * M*V^2, { rw=V}
now energy at an instant when x length is unrolled.,

mass per unit length= M/L = k
energy at this instant is 3/4 * (M- x*M/L)*v^2
equating these two we get

v^2 = (L/L-x) * V^2

v= sqrt(L/L-x)*V
sqrt(L-x)*dx = Vsqrt(L)*dt

now integrate, as x varies from 0 to L , L-x varies from L to 0,
on integrating you'll get
t = 2L/3V

hope this is correct ;)

karthik2007

Brilliant answer Nishant

rohith291991

i have a doubt...u got v= sqrt(L/L-x)*V but when u put x=L we get final velocity to be infinity....but actually it must be zero... seems out of place....also how are u equating initial kinetic energy with final KE ???

rohith291991

ok i got it...at the end of the rolling the last part of the hose is tugged with a huge force...so the velocity changes from an extremely large value to zero in a short time....great work nishant!! i didnt use work-KE theorem properly......there can be no force acting...so KE must be conserved...but i didnt conserve KE...i "conserved" *cough* velocity...

lol... so once again congrats....good work..

nishantsingh89

@karthik, rohit

thnx for acknowledging my efforts :)

Conjurer

Awesome nishanth , I dont know the answer as answers are not given in that paper but it sure looks good.So no reason to doubt. :D

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