What should be the minimum force P to be applied to the string so that block of mass m just begins to move up the frictionless plane?

Explanation

From force diagram of pulley.
`P+P cos theta=T`
From force diagram of block
`T gt mg sin theta`
or ` P+P cos theta gt mg sin theta`
or `P gt(mg sin theta)/(1+ cos theta)`
`:. P_(min)=(mg sin theta)/(1+cos theta)`