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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

  1. $0.953$ $\text{Ns}$
  2. $1.403$ $\text{Ns}$
  3. $0.814$ $\text{Ns}$
  4. $1.172$ $\text{Ns}$
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