In figure `m_1=5 kg, m_2=2kg and F=1N.` Find the acceleration of either block. Describe the motion of `m_1` if the string breaks but F continues to act.

Explanation

From the free body diagram (. ) we have
` m_1 a +F-T=-`
` rarr T=m_1a+F`

From the free body diagram (. 2)
` m_2a+T-m_2g=0`
`rarr m_2a+m_1+F-m_2g=0` (from i.)
`rarr a(m_1+m_2)+(m_2g)/2-m_2g=0`
` [because F= (m_2g)/2]`
`rarr a(m_1+m_2)= (m_2g)/2`
` rarr Acceleration of mass,
`a= (m_2g)/(2(m_1+m_2))` towards right.