Consider the situation shown in figure. All the surfaces are frictions and the string and the pulley are light. Find the magnitude of the acceleration of the two blocks.

Explanation

Mass per unit length `= 3/30 kg/cm`
` = 0.10 kg/cm`
Mass of 10 cm part `=m_1 =1 kg`
Mass of 20 cm part `= m_2= 2 kg`

Let F= contact force between them.
From the free body diagram
`F=20-10=0` ........i
` and 32-F-2a=0` ...........ii
From equatiions i. and ii.
` 3a-12=0`
` rarr a= 12/3=4m/s^2 `
` Contact force F=20+la`
`=20+1xx4=24N`