Three uniform blocks A, B and C respectively of mass m, $$m2$$ and m of different densities and dimensions are placed over each other as shown in the figure. The coefficients of friction are shown. Blocks placed in a vertical line are made to move towards right with same velocity at the same instant. Find the time (in$$ $$sec$$$$) taken by the upper block A to topple from the middle block B. Assume that blocks B and C don’t stop sliding before A topples from B. (given$$ L $$=$$ $$36$$ m, μ $$=$$ $$0.4$$ and g $$=$$ $$10$$ $$m/s2$$ $$)

Question

Three  uniform blocks  A,  B  and  C  respectively of  mass  m,  $$m2$$  and  m  of  different  densities  and  dimensions  are  placed  over  each  other  as shown  in  the  figure.  The  coefficients  of  friction  are  shown. Blocks  placed  in  a  vertical  line  are  made  to  move  towards   right with same velocity at the same instant. Find the time (in$$ $$sec$$$$) taken by the upper block A to topple from the middle block B. Assume that blocks B and C don’t stop  sliding before A topples from B. (given$$ L $$=$$ $$36$$ m,  μ $$=$$ $$0.4$$ and g $$=$$ $$10$$ $$m/s2$$ $$)

Infinity Learn · Accepted Answer

Since μ$$4$$<μ$$2$$<μ, the upper block will move faster than the middle block and hence force of friction on upper block is towards left  ∴   $$f=$$μ$$4$$ mg∴   $$aA=$$μ$$g4$$  leftwardf'$$=$$μ$$2(m+m2)g=34$$  μmg ∴   $$aB=$$μg  (leftward)∴   $$aA/B=34$$  μg  $$(rightward)For$$ sliding down the block B, A has to move a distance  $$3L8Relative$$ to block $$B.3L8=12$$  $$34$$  μ$$gt2$$  ∴   $$t=L$$μ$$g=3$$  $$sec$$

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