In the arrangement as shown, mB = 3m, density of liquid is r and density of block B is 2r. The system is released from rest so that block B moves up when in liquid and moves down when out of liquid with the same acceleration. Find the mass of block A.

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74m

2 m

92m

94m

answer is D.

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Detailed Solution

Acceleration when block B is in the liquid, a1=mAg−(mBg−upthrust)(mA+3m)⇒=mAg−3mg−3m2ρρg(mA+3m)(↑). Acceleration when block B is outside of the liquid, a2=3mg−mAg(mA+3m)(↓). Given a1 =a2, we get, mAg−32mg=3mg−mAg⇒2mAg−92mg⇒mA=94m.

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