A cylinder of mass m is kept on the edge of a plank of mass 2m and length 12m, which in turn is kept on smooth ground.coefficient of friction between the plank and the cylinder is 0.1. The cylinder is given an impulse , which imparts it a velocity 7m/s but no angular velocity.Find the time after which the cylinder falls off the plank.

please any one , give the solution to my question.

yes the plank is frictionless.

the question is as given above.   no more doubts please.

i want the solution.

Is the answer 4 ? Friction is an internal force.. So no movement of centre of mass of plank + cylinder system.. So when it rolls off, the the position of the plank, will be at (2,0), considering initial position of ball to be at origin.. This you get by conserving position of centre of mass.. Now only force acting on plank is friction due to cylinder, which is umg, where u is coeff of friction. Acceleration is ug/2

(1/2)(ug/2)t^2=4

Putting values  you get t=4.. Only thing is, I didn't make use of the initial velocity.. Am I missing something here?

the answer is 2.25 sec.                     i want the solution.

why no body is ready?

hey goiitians whats this ?         i am waiting for the solution from 2 days .         why no one helping me? try the

problem once. its from arihanth actually.

i think its just a waste of time .........     yaar............

ok.. as a rule... i never solve questions first time unless my help is not enough the first time.

so try this and see if you get it. otherwise i will solve it.

for any body to roll, it requires a torque. this torque is usually provided by friction. so the friction b/w the plank and cylinder will casue the cylinder to

1) decelerate

2) roll in a clocwise sense.

friction will act to the left (all this in reference to your figure).

this friction stops acting when the cylinder stops rolling. so what will happen is that the VELOCITY  in the right direction will decrease, and at the same time the CLOCKWISE angular velocity will increase, until v =rw.

now the real problem is : will this v = rw before the cylinder falls off the plank or not?

the problem is very very long, and we will have to do this in 2 cases.

in the first case, we say that the cylinder continues to decelerate till the end. this is the easier case, so try it first. frictional force can be found, and use newtons second law and write torque equations. if the answer is absurd, like imaginary roots etc, then take second case.

assume that it decelerates for t seconds and from then v = rw..

well its long.. but this is the only method i know.

shit this question is a very long one. i guess you will be disappointed that i did not solve it.. and now that i see it i dont even want to.. lol.

shreyas

"SINCE THE SPHERE DOES NOT ROLL"

this is wrong. the sphere must and will rotate.

trust me arihant problems are not one step problems. this one surely is the longest one i  have ever seen.

if your method is so simple, why dont u calculate the answer and see if it matches.