Q.

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.

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a

2l3a+μg

b

2la+μg

c

2l2a+μg

d

l3a+μg

answer is A.

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Detailed Solution

Equation of motions of (A + C) and B asT−f=ma1T−μmg=ma1  ………(i)T−2μmg=2ma ………(ii)T=2μmg+2ma from (i)  2 μmg +2ma− μmg =ma1a1=μg+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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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.