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A cubical block is floating in a liquid with half of its volume immersed in the liquid . When the whole system accelerates upward with the net acceleration of g/3. The fraction of volume immersed in liquid will be ?

A cubical block is floating in a liquid with half of its volume immersed in the liquid . When the whole system accelerates upward with the net acceleration of g/3. The fraction of volume immersed in liquid will be ?

Grade:12

5 Answers

Pushkar Prateek
23 Points
7 years ago
Apply Archimedes principle when system is at rest,
 
weight of the block = Buoyant force by liquid
\rhob V g = \rhoL V/2 g
so
\rhob/\rhoL =1/2 
 
Now, when system accelerates upward with g/3 draw FBD of the block, Buoyant force upwards and weight downwards
Being part of the system block also goes up with g/3, 
making equation from 2nd law of motion
 
Fb - Mg = Mg/3
Fb = 4Mg/3
 
\rholiquid Vvolume of block immersed  g  = 4/3 \rhoblock Vtotal volume of the block   g
 
hence 
Vvolume of block immersed / Vtotal volume of the block   = 2/3
Aayush Garg
36 Points
7 years ago
Dear He/She,..........................Your answer is wrong. There is no effect of acceleration....................... 😊.....................
Aayush Garg
36 Points
7 years ago
Answer : Faction of volume immersed will be same, i.e., half of block will be immersed..........................
Rishesh Gangwar
31 Points
5 years ago
Fraction of volume immersed in the liquid 
Vin=(ρσ)V
 i.e. it depends upon the densities of the block and liquid. So there will be no change in it if system moves upward or downward with constant velocity or some acceleration.
Mr Mujtaba
15 Points
5 years ago
Upward acceleration just causes the acceleration due to gravity increases by some value, but since the term of 'g'
gets cancelled out in the buoyancy equation.
Volume immersed × w × g = Total volume × cube × g
So, increasing it will not have any effect on the immersed volume.

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