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A particle of mass m is placed at rest on the top of a smooth wedge of mass M,which in turn is placed at rest on a smooth horizontal surface.If hbe the height of wedge and θ is the inclination,then the distance moved by the wedge as the particle reaches the foot of the wedge is ______________
Dear sindhuja
there is no external horizontal force is acting on the system so center of mass will not move in x direction.
base of the wedge = hcotΘ
let the left lower corner of wedge is origin and wedge move by x' distance ,and center of mass of wedge is at x1 distance from origin
so (mhcotΘ +Mx1)/(m+M) ={m(x'-hcotΘ) +M(x1+x')}/(m+M)
or mhcotΘ +Mx1 =m(x'-hcotΘ) +M(x1+x')
or 2mhcotΘ =(m+M)x'
x'= 2mhcot/(m+M)
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