First slide
Fluid statics
Question

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.

 

 

Moderate
Solution

Acceleration when block B is in the liquid, a1=mAg(mBgupthrust)(mA+3m)=mAg3mg3m2ρρg(mA+3m)(). Acceleration when block B is outside of the liquid, a2=3mgmAg(mA+3m)(). Given a1 =a2, we get, mAg32mg=3mgmAg2mAg92mgmA=94m.

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