Two blocks of masses `m_(1)` = 3 kg and `m_(2) = (1)/(sqrt3)` kg are connected by a light inextensible string which passes over a smooth peg . The blocks rest on the inclined smooth planes of a wedge and the peg is fixed to the top of the wedge . The planes of the wedge supporting `m_(1)` and `m_(2)` are inclined at `30^(@)` and `60^(@)` respectively , with the horizontal. Calculate the acceleration of masses and the tension in the string .

Explanation

As `m_(1) g "sin" 30^(@) gt m_(2) g "sin" 60^(@)` , so `m_(1)` will be moving downward and `m_(2)` upward with the same acceleration as the string is inextensible . The forces and their resolved

components along and perpendicular to the incline are shown in Fig . 7.57 . The equations of motion are :
`m_(1) g "sin" 30^(@) - T = m_(1) a " " ....... (i) `
`T - m_(2) g "sin" 60^(@) = m_(2)a " " .... (ii)`
Adding and solving ,
`a = (m_(1) g "sin" 30^(@) - m_(2)g "sin" 60^(@))/((m_(1) + m_(2)))`
`((3 xx (1)/(2) - (1)/(sqrt3) xx (sqrt3)/(2)) xx 10)/((3 + (1)/(sqrt3)))`
= `2.8 m// s^(2)`
Substituting for a in eqn .(i)
`T = m_(1) g "sin" 30^(@) - m_(1) a`
`= 3 xx 10 xx (1)/(2) - 3 xx 2.8`
`= 6.6 N`