Find the acceleration of each block

Options

A. `2/15 m//s^(2)`
B. `62/15 m//s^(2)`
C. zero
D. `2/5 m//s^(2)`

Answer

C

Explanation

Tendency of 2kg block is of coming down
and of 1kg is of going up

Where `F_(1)` is friction between 1kg and 2kg block and `F_(2)` is friction between 2kg and inclined surface.
For 2kg block `2xx10xx1/2-T-F_(1)-F_(2)=2a`
For 1 kg block `T-1xx10xx1/2 xxF_(1) =a`
`rArr ` Add both `10-5-2F_(1)-F_(2)=3a`
`5-2F_(1)-F_(2)=3a`
The max. value of `F_(1)=0.1xx1xx10(sqrt(3))/2=(sqrt(3))/2`
`F_(2 max) =3xx10xx0.2xx(sqrt(3))/2 =3sqrt(3)`
Max `(2F_(1)+F_(2))=sqrt(3)+3sqrt(3)=4sqrt(3) =5.1`
N
`rArr ` static friciton will fact. `rArr a=0`