Physics
Fluid-Mechanics
Easy

Question

A candle of diameter d is floating on a liquid in a cylindrical container of diameter D(D>>d) as

  1. Remain at the same height
  2. Fall at the rate of 1 cm / hour
  3. Fall at the rate of 2 cm / hour
  4. Go up the rate of 1 cm / hour

The correct answer is: Fall at the rate of 1 cm / hour


    text  Initially  end text A 2 L rho subscript 1 g equals A L rho subscript 2 g
text  Here  end text rho subscript 1 text  and  end text rho subscript 2 text  are densities of candle material and  end text not stretchy rightwards double arrow rho subscript 1 over rho subscript 2 equals 1 half
text  Let  end text y subscript 1 text  be the height of candle at an instant and  end text y subscript 2 text  be the length of immersed part.  end text
table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell text  here  end text y subscript 1 over y subscript 2 equals 2 end cell row cell text  As  end text fraction numerator d y subscript 1 over denominator d t end fraction equals 2 cm divided by hr end cell row cell fraction numerator d y subscript 2 over denominator d t end fraction equals 1 cm divided by hr end cell row cell s o space c a n d l e space m o v e s space d o w n space a t space 1 space c m divided by space h r end cell end table

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