Rotational and collision problem

[sunnypic143]

Homework Statement

This question I came across in mechanics book by Bostock Chandler
> A uniform disc, resting on a smooth horizontal table, has mass 'm', radius 'a' and centre C. A particle of mass 'm', moving across the table with speed 'v', strikes a point A on the circumference of the disc when traveling at right angles to AC. If the particle adheres to the disc, find the initial velocity of C.

Homework Equations

Both the particle and the disc have same mass, so after the event velocity of the common centre of mass will be v/2. thereafter applying conservation of angular momentum about the common center of mass i get the velocity of C as v/4, but the answer specified in the book is 2v/5. Where am i going wrong

 

[tiny-tim]

Hi sunnypic143!

yes, I applied conservation of angular momentum about A, and got the same result …

(v - 2w)/a ma²/2 = maw, so v - 2w = 2w.

it looks as if the book has used 2ma² for the moment of inertia of a disc, instead of ma²/2 … v - 2w = w/2.

Is this is the latest edition of the book? Maybe a later one has a correction (and which book by Bostock and Chandler is it)?​

 

[sunnypic143]

hey tim thanks 4 the reply

this is exactly what i thought!

but i have gr8 respect for the authors, probably they implied a different orientation of the disc
say xz plane(if we assume table to be xy) and the particle travels along y axis

or something else like that and they failed to convey it properly
if anything else occurs to you be sure to reply
i wouldn't buy that the authors took moment of inertia as 2ma^2. Sounds too dumb of them if they did. Anyway thanx

Btw the book is 'further mechanics and probablity' published by stanley thornes