List of top Applied Mechanics and Design Questions on Impulse and momentum (linear and angular)

A rigid homogeneous uniform block of mass 1 kg, height $h = 0.4$ m and width $b = 0.3$ m is pinned at one corner and placed upright in a uniform gravitational field ($g = 9.81$ m/s$^2$), supported by a roller as shown. A short duration impulsive force $F$, producing an impulse $I_F$, is applied at a height $d = 0.3$ m from the bottom. Assume all joints to be frictionless. The minimum value of $I_F$ required to topple the block is ________________.