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NEET2005PhysicsMechanical Properties of FluidsActual

A candle of diameter d is floating on a liquid in a cylindrical container of diameter D(D>>d) as shown in figure. If it is burning at the rate of 2 ~cm / hour then the top of the candle will

Options

  1. Aremain at the same height
  2. Bfall at the rate of 1 ~cm / hour
  3. Cfall at the rate of 2 ~cm / hour
  4. Dgo up at the rate of 1 ~cm / hour.

Correct answer

B. fall at the rate of 1 ~cm / hour

Step-by-step solution

Initial weight of the candle = weight of liquid displaced _C V_C g= _L (volume displaced) g _C ( d 2 )^2 2 L g= _L d^2 2 L g _C _L = 1 2 When 2 ~cm has been burnt, total length =2 L-2 But _C(2 L-2)= _L(L-x) aligned & _C 2(L-1)=2 _C(L-x) & x=1 ~cm . aligned [Using eqn. (i)] Outside also it has decreased 1 ~cm as the total decrease is 2 ~cm . The level of the candle comes down at half the rate of burning.

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