Figure shows block A a motor C mounted on a with combined mass m and another block B of mass $$2m$$. Block B is attached to shaft of motor with a light inextensible string. Motor is switched on at t $$=0$$ and string starts winding on its shaft and block B starts moving at acceleration a. If initial separation between blocks is l then find the time after which the two bodies will collide. The friction coefficient between blocks and ground is μ.

Question

Figure shows block A a motor C mounted on a with combined mass m and another block B of mass $$2m$$. Block B is attached to shaft of motor with a light inextensible string. Motor is switched on at t $$=0$$ and string starts winding on its shaft and block B starts moving at acceleration a. If initial separation between blocks is l then find the time after which the two bodies will collide. The friction coefficient between blocks and ground is μ.

Infinity Learn · Accepted Answer

Equation of motions of (A$$ $$+$$ $$C) and B asT−$$f=ma1T$$−μ$$mg=ma1$$  ………(i)T$$−$$2$$μ$$mg=2ma$$ ………$$(ii)T=2$$μ$$mg+2ma$$ from $$(i)  $$2$$ μmg $$+2ma$$− μmg $$=ma1a1=$$μ$$g+2arelative$$  acceleration of B w.r.t (A+C) $$aBA=a+a1=3a+$$μgtime taken to cover a length l is $$t=2laBA=2l3a+$$μg

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