Two smooth blocks of same mass are connected by an inextensible and massless string which is passing over a smooth pulley are kept in a lift is going down with

acceleration 'a' as shown in the fig What should be the value of a (in `m//s^(2))` so that acceleration of block A w.r.t. ground will be minimum? `(g=10m//s^(2))`

Answer

2

Explanation

Rightoword acceleration of w.r.t lift is
`a_(1)=(m(g-a))/(m+m)=(g-a)/(2)` w.r.t ground
`a_(A)=sqrt(a^(2)+((g-a)/(2))^(2))=sqrt((5a^(2))/(4)-(ga)/(2)+(g^(2))/(4))`
`a_(A)` is min when `(da_(A))/(da)=0`
`(5a)/(2)-(g)/(2) =0rArra =g//5 =2ms^(2)` .