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.

Find out the value(s) of theta of the inclined plane such that the mas

1.	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» 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)]`