Saved Bookmarks
| 1. |
A uniform disc of radius R has a hole cut out which has a radius r. The centre of hole is at a distance (R )/(2) from the centre of disc. The position of centre of mass is shifted through a distance x from 'O' find x. If in this question the values of R = 6 m and that if r = 1 m, calculate the valueof shift from 'O' and state whether it is towards left or right of O. |
|
Answer» `(R^(2)r)/(2(R^(2)-r^(2))),(3)/(37)m` TOWARDS left of 'O' (t = thickness) Mass of scooped out discc `=pir^(2)trho` Mass of remaining disc `=pi(R^(2)-r^(2))trho` Then, `pi(R^(2)-r^(2))trhoxx X=pir^(2)trho(R)/(2)` or `x=(r^(2)R)/(2(R^(2)-r^(2)))`  Now `x=(r^(2)R)/(2(R^(2)-r^(2)))` Here `r=1m` `R=6m` `THEREFORE x=((1)^(2)xx6)/(2(36-1))=(3)/(35)m` towards left of centre. |
|