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# Figure shows a small block A of mass m kept at the left end of a plank B of mass M=2m and length λ. The system can slide on a horizontal road. The system is started towards right with the initial velocity v. The friction coefficients between the road and the plank is 1/2 and that between the plank and the block is 1/4(b) displacement of block and plank with respect to ground till that moment? Open in App
Solution

## Ref. image ILet a1 and a2 be acceleration of mass m and 2m also a1>a2 so mass m moves on 2m.Let after time t mass m is separated from 2m.using equation of motion. during this time, mass m covers vt+12a1t2 & 5m=vt+12a2t2 for mass m to separate from 2m, we have vt+12a1t2=vt+12a2t2+1Ref. image IIAs 12μ1=14μ2μ=μ2from free body diagram we have, ma1+μ2R=0ma1=−μ2mg=μ2ga1=−5μagain , (2m)a2+μ(2m+m)g−(μ2)mg=0⇒2(2m)a2+2μ(2m+m)g−μmg=0⇒2(2m)a2=μmg−2μmg−2μmga2=−μmg−2μ(2m)g2(2m)Substituting values of a1 & a2 in eq. (1)t=4(2m)l(2m+m)μg   Suggest Corrections  0      Related Videos   PHYSICS
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