Question

A disc of radius 'r' is removed from the disc of radius 'R' then

a. the minimum shift in centre of mass is zero

b. the maximum shift in centre of cannot be greater than $\frac{r^2}{(R+r)}$

c. Centre of mass must be lie where mass exists

d. the shift in centre of mass is $\frac{r^2}{(R+r)}$

• A. a ,b are correct
• B. b,c are correct
• C. a, b, d are correct
• D. a, b, c, d are correct

Answer 1

The correct option is A

a ,b are correct

If we remove the smaller disc from the bigger disc such that both are concentric, then there is no shift in

cenre of mass. So minimum shift in centre of mass is zero. The value of shift in centre of mass depends

on the position from where we remove smaller disc from the bigger disc .

To get maximum shift in centre of mass , the smaller has to removed as below

$△x_{cm}=\frac{m_1{x}_1-m_2{x}_2}{m_1-m_2}$

$△x_{cm}=\frac{\sigma \left(\pi R^2\right)\left(0\right)-\sigma \pi r^2(R-r)}{\sigma \pi R^2-\sigma \pi r^2}$

$△x_{cm}=-\frac{r^2(R-r)}{(R^2-r^2}$

$△x_{cm}=-\frac{r^2}{(R+r)}$