Two block `m_(1) ` and `m_(2)` are placed on a smooth inclined plane as shown in figure. It they are released from rest.
Find `:`
(i) acceleration of mass `m_(1)` and `m_(2)`
(ii) tension in the string
(iii) net force on pulley exerted by string

Explanation

F.B.D. of `m_(1) ` `:`
`m_(1) g sin theta - T = m_(1) a `
F.B.D. of `m_(2) :`
`T -m_(2) g sin theta = m_(2) a `
`T -1. ( sqrt(3))/( 2) g = 1 .a` ...(ii)
Adding eq. (i) and (ii)
we get `a = 0 `
Putting this value in eq. (i) we get

`T = ( sqrt(3) g )/( 2)` ,
F.B.D. of pulley
`F_(R ) = sqrt( 2) T `
`F_(R ) = sqrt((3)/( 2)) g `