A machinist starts with three identical square plates but cuts one corner from one of them, two corners from the second and three corners from the third. Rank the three according to the `x`-coordinate of their centre of mass, from smallest to largest.

Options

A. `3,1,2`
B. `1,3,2`
C. `3,2,1`
D. `1` and `3`tie, then `2`

Answer

B

Explanation

Ans. (2)
Let mass of full plate be `M` and cutted square plate be '`m`', `X_(cm)` of cutted piece either is `pit (-a)` ot `(+a)`
`(i)` `X_(cm)=(M(0)-m(-a))/(M-m)=(ma)/(M-m)`
`(ii)` `X_(cm)=(M(0)-m(-a)-m(-a))/(M-2m)=(2ma)/(M-2m)`
`(iii)` `X_(cm)=(M(0)-m(-a)-m(-a)-m(-a))/(M-3m)=(ma)/(M-3m)`
`X_(cm)` is least for `(i)` and `X_(cm)` for `(ii)` & `(iii)` will be higher
Ans either `1,3,2` or `1,2,3`
Also `Mgt4m`
so `1,3,2`