Grade 12Mechanics

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 ?

Aayush Garg

9 Years agoGrade 12

5 Answers

Pushkar Prateek

9 Years ago

Apply Archimedes principle when system is at rest,

weight of the block = Buoyant force by liquid

$\rho$ b V g = $\rho$ L V/2 g

$\rho$ b/ $\rho$ L =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 2^nd law of motion

F_b- Mg = Mg/3

F_b= 4Mg/3

$\rho$ _liquid V_{volume of block immersed} g = 4/3 $\rho$ block Vtotal volume of the block g

hence

V_{volume of block immersed /}Vtotal volume of the block = 2/3

Aayush Garg

9 Years ago

Dear He/She,..........................Your answer is wrong. There is no effect of acceleration....................... 😊.....................

Aayush Garg

9 Years ago

Answer : Faction of volume immersed will be same, i.e., half of block will be immersed..........................

Rishesh Gangwar

7 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

7 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.