A rigid homogeneous uniform block of mass $1$ $\text{kg}$, 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 in the configuration shown in the figure. A short duration (impulsive) force $F$, producing an impulse $I_{F}$, is applied at a height of $d = 0.3\: m$ from the bottom as shown. Assume all joints to be frictionless. The minimum value of $I_{F}$ required to topple the block is
- $0.953$ $\text{Ns}$
- $1.403$ $\text{Ns}$
- $0.814$ $\text{Ns}$
- $1.172$ $\text{Ns}$