In fig two block of mass `m_(A) and m_(B)` are rotating at radius `r` kept on a rough table consider friction `(mu)` between all the contact surface pulley is frictionless determine the angular speed of the turn table for which the blocks just begin to slide

Explanation

Equation for block `B` :
`sum F_(x) = T + mu_(s) m_(A) + m_(B) g + mu_(s)m_(A)g - m_(B) r omega^(2) = 0 `

Equation for block `A` :
`sum F_(x) = T - mu_(s) (m_(A)) g - (m_(A)r omega^(2)) = 0` ...(i)
From equation (i) and (ii) , we climinate `T` as obtain
`2mu_(s) m_(A) g +mu(m_(A) - m_(B)) = (m_(B) - m_(A)) r omega^(2)`
`omega = [(mu_(s)g(3m_(A) + m_(B)))/(r(m_(B) - m_(A)))]^(1//2)`