A  cyllinder of mass M and radius h/2  is connected to a string as shown. What is the ratio m/M such that the cyllinder tilts

A.1/2

B.1/4

C.1/3

D.2/3

Ans:c  How?

Apply the condition for Toppling, 

The Tension tends to create a clockwise torque about the COM. This causes the normal reaction to shift to the right , and in the limiting case, torque due the normal reaction = 0,when it passes through P

Now, torque due to tension = Th  (about P)

Torque due to mg = Mgh/2  (about P )

Now, in the limiting case when the body is just about to topple,

Mgh/2 = Th

Mg/2 =T

Now, Consider the acceleration of block m , a

T-mg= ma

But, T is also equal to Ma , because in the absence of any friction, it would have been T=Ma

Therefore a=g/2

i.e. T-mg = mg/2

T = 3mg/2

since T=Mg/2

Mg=3mg

m/M = 1/3