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Question

Two identical discs of mass M and radius R are connected by a light rod. The assembly rests at a corner, the vertical wall is smooth and there is sufficient friction on the floor to ensure pure rolling of disc B. The system starts from position θ=0. Find the velocity of the midpoint of the rod when θ=60o.
1486721_a1608a8cabd2476db1b257548970303b.png

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Solution

VAcosθ=VBsinθ(1)VA=VBsinθNow,wall=Δkmg(llcosθ)=12mV2A+12mV2B+12[mR22]×V2BR2atθ=60mgl2=12mV2A+12mV2B+mV2B4gl2=V2A2+34V2Bgl=V2Btan2θ2+34V2Agl=V2Br32+34V2Bgl=94V2B49×10×60100=V2BVB=249=243Va=243×3=243Now,Vacidpoint=(VA2)2+(VB2)2=244×3+244×9=63+69=2+23=23
Which is the required answer.

1221161_1486721_ans_4cf431854b0e4874a1b150441eb6af03.png

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