Find the acceleration of the two blocks. The system is initially at rest and the friction coefficient are as shown in the figure?

Explanation

`f_(max)=50N`
`therefore f le 50N`

(i) If they move together `a=101/20=5.05m//s^(2)`
(ii) Check friction on B
`" "f=10 times 5.05=50.5` (required)
`50.5 gt 50` (therefore required `gt` available)
Hence they will not move together
(iii) Hence they move separately so kinetic friction is involved.

`therefore " for " a_(A)=(101-50)/10=5.1 m//s^(2)`
`rArr a_(B)=50/10=5m//s^(2)`
Also `a_(A) gt a_(B)` as force is applied on A.