In the system shown in figure, the block A is released from rest. Find

the acceleration of both blocks ‘A’ and ‘B’.

Answer

`g/3hat(i)-g/3hat(j)," "g/3hat(i)`

Explanation

Let acceleration of blocks in x & y directions are

Taking both blocks as a system
`T=2mb . . . .. .. (i)`

Taking A block :
`mg – T = ma " " . . . . . . . . . (ii)`
From equations (i) & (ii) ,
`ma + 2 mb = mg`
` a + 2 b = g" " .. . . . . . . . .(iii)`
From string constraint ,
`a = b" " . . . . . . . . . . .(iv)`
From equations (iii) & (iv),

`a=b=(g)/(3)`
hence, acceleration of block A
`a_(A)=bhat(i)-ahat(j)" "a_(A)=g/3hat(i)-g/3hat(j)`
acceleration of block B
`a_(B)=bhat(i)=(g)/(3)hat(i)`