Easy center of mass/toppling question?

I am studying the edexcel A level M2 mathematics module and came across this question that i don't know how to do.Even the book doesn't have any material to help me out with this sort of questions.

Sorry If i've posted this in the wrong section.Since it said 'classical physics' so i thought it should go here :P







A thin uniform rectangular metal plate ABCD of mass M rests on a rough plane inclined at an angle σ to the horizontal.the plate lies in a vertical plane containing a line of greatest slope of the plane, with the edge CD in contact with the plane and C further up the plane than D, as shown in the figure.The lengths of AB and BC are 10cm and 30cm respectively.The plane is sufficiently rough to prevent the plate from slipping.



a)Find, to the nearest degree, the greatest value which σ can have if the plate does not topple.



A small stud of mass m is fixed to the plate at the point C



b)Given that tanσ=1/2, find, in terms of M, the smallest value of m which will enable the plate to stay in equilibrium without toppling.



I could do a) but got stuck at b).I tried applying principle of moments for m but all to no avail.



Answers- a) 18' b) 0.25M



Thanks in advance :)