a plank of mass 2kg and length 1m is placed on horizontal floor, a small block of mass 1kg is placed o top of the plank,at its extreme end. the co efficient of friction between plank and floor is 0.5 and that between plank and block is 0.2 .if a horizontal force=30N starts acting on the plank to right,the time after which,the block will fall off the plank?

Dear akash

let at time t small block cover a distance x

and for amall block to fall plank must cover (x+1) m in time t

accelarion of small block=2/1 =2

acceleration of plank =(30-15-2)/2 =13/2

so x= 1/2 *a1 *t^{2   =}   t^{2 .................1}

^and

x+1 =1/2 *a2*t²

^{put value of x from equation 1}

 t² +1 =1/2 *a2*t²

t=2/3 sec

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