In figure `m_(1)= 1 kg` and `m_(2)= 4 kg` Find the mass `m` of the hanging block which will prevent the smaller block from slipping over the triangular block .All the surface are frictionless and the string and the pulleys are light

Explanation

`a = ("Net pulling force")/("Total mass")`

`a = (M g)/(m_(1) + m_(2) + M)` …(i)
`N cos 30^(@) = m_(1) g` …(ii)
`m_(1)` `N sin 30^(@) = m_(1) a` …(iii)

From Eqs. (ii) and (iii), we get
`a = g tan 30^(@) =(g)/(sqrt3)`
Substituting this value in Eq. (i)we get,
`M = 6.83 kg`