Figure shows an arrangement of pulleys and two blocks. All surfaces are frictionless . All pulleys and strings are massless. All string are smooth and massless.

The acceleration of block `A` is `:`

Options

A. `(2g)/(9)`
B. `(g)/(9)`
C. `(g)/(5)`
D. none of these

Answer

A

Explanation

`T=2ma`
`mg-2T=(ma)/(2)`
`mg-4ma=(ma)/(2)`
`mg=(9ma)/(2)`
`a=(2g)/(9)`
`T=(4mg)/(9)`
`N_(1)=ma=(2ma)/(9)`
`N_(2)=mg+2T`
`N_(2)=mg+2T`
`=mg+(8mg)/(9)=(17mg)/(9)`.