A block of mass `m_(1)` rests on a horizontal table. A string tied to the block is passed on a frictionless pulley fixed at the end of the table and to the other end of string is hung another block of mass `m_(2)`. The acceleration of the system is

Explanation

We can draw free body diagrams for each individual part of the system. When the nail fixed on the table gets removed, the system of two bodies moves with an acceleration (a), as shown in figure

Equations of motion can be written as
`m_2g- T=m_2a`
`T=m_1a`......(ii)
`R=m_1g`.....(iii)
Adding (i) and (ii) we get
`m_2g= (m_2+m_1) a or a=(m_2g)/((m_2+m_1))`
Putting the given values , we get
`a=(8 times 10)/((8+12))=4ms^-2`