• # question_answer Rectangular block B, having height h and width d has been placed on another block A as shown in the figure. Both blocks have equal mass and there is no friction between A and the horizontal surface. A horizontal time dependent force $F=kt$is applied on the block A. At what time will block B topple? Assume that friction between the two blocks is large enough to prevent B from slipping. A) $\frac{dgm}{2kh}$        B)        $\frac{2dgm}{kh}$ C) $\frac{dgm}{kh}$          D)        $\frac{3dgm}{2kh}$

[b] Acceleration $a=\frac{F}{2m}=\frac{kt}{2m}$ The force diagram of block B in reference frame attached to A is shown in figure. The normal force passes through left edge at the instant the block is about to topple. The block will be on verge of toppling when $ma\frac{h}{2}=mg\frac{d}{2}$ $m\frac{kt}{2m}\frac{h}{2}=mg\frac{d}{2}$                 $\therefore \,\,\,\,t=\frac{2dgm}{kh}$