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

`2Ma+mg sin theta - T=0`
`rarr T= 2Ma+Mg sin theta ` ….i.
`Now 2T+2Ma-2Mg=0`
From equation i. `
`2(2Ma+Mg sin theta)+2Ma-2Mg=0`
` rarr 4Ma +2Mg sin theta + 2Ma- 2Mg = 0`
` rarr 6Ma + 2Mg sin 30^0 +2Mg=0`
` 6Ma=Mg`
`rarr as= g/6`
Hence acceleration of mas,
` M=2a=2xx g/6 `
` =g/3 up the plane.