Find the mass M of the hanging block in figure which will prevent the smaller block from sliping over the triangular blcok. All the surfaces are frictions and the strings 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.