Find out the value(s) of `theta` of the inclined plane such that the mass m remains at rest on the wedge of mass `M_(2)` as shown in figure-2.215. Friction between the small block and the wedge plane is `mu` and all other surface are smooth.

Answer

`[sinalpha_("max")-sqrt(4p^(2)q^(2)-4(p^(2)+q^(2))(r^(2)-p^(2))-2qr)/(2(p^(2)+q^(2)))`
where `p=m(g-mua),q=m(a+mug),r=M_(1)(a-g)" and "a=(M_(1)g)/(M_(1)+M_(2)+m)`
`sinalpha_("min")=sqrt(4l^(2)k^(2)-4(l^(2)+k^(2))(n^(2)-l^(2))-2kn)/(2(l^(2)+k^(2)))`,
where `l= m(a-mug),k=m(g+mua),n=M_(1)(a-g)" and "a=(M_(1)g)/(M_(1)+M_(2)+m)]`