Three blocks of masses `m_1, m_2 and m_3` are connected as shown in the figure. All the surfaces are frictionless and the string and the pulleys are light. Find the acceleration of `m_1`

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`