Two blocks 4 kg and 2 kg are sliding down an incline plane as shown in fig The acceleration of 2 kg block is:

Options

A. `1.6 m//s^(2)`
B. `2.6 m//s^(2)`
C. `3.6m//s^(2)`
D. `4.6 m//s^(2)`

Answer

B

Explanation

Force on 4 kg block sliding down the plane is:
`F_(1)=m_(1)g(sin theta-mu_(1) cos theta)`
`=4xx9.8(sin 30^(@)-0.3 cos 30^(@))`
`=9.4 N`
Force on 2 kg block sliding down the plane is:
`F_(2)=m_(2)g(sin theta-mu_(2) cos theta)`
`=2xx9.8(sin 30^(@)-0.2 cos 30^(@))=6.4N`
Total force `=F_(1)+F_(2)=9.4+6.4=15.8N`
`:."Acceleration"=(15.8)/6=2.6 m//s^(2)`
Note: Acceleration of block `m_(1)` is less than that of block `m_(2)` hence, both blocks will move together.