A candle of diameter `d` is floating on a liquid in a cylindrical container of diameter `D(D lt lt d)` as shown in figure. If is burning at the rate of `2 cm//h` then the top of the candle will :

Options

A. remain at the same height
B. fall at the rate of 1 cm/hour
C. fall at the rate of 2 cm/hour
D. go up at the rate of 1 cm/hour

Answer

B

Explanation

Initial weight of the candle = weight of liquid displaced
`rho_(C)V_(C)g=rho_(L)` (volume displaced) g
`rArr rho_(C)pi((d)/(2))^(2)2L=rho_(L)pi (d^(2))/(2) Lg rArr (rho_(C))/(rho_(L))=(1)/(2)" ….(i)"`
When 2 cm has been burnt, total length `=2L-2" But "rho_(C)(2L-2)=rho_(L)(L-x)`
`rho_(C)2(L-1)=2rho_(C)(L-x)" "`[Using eqn. (i)]
`therefore" "x=1 cm`.
Outside also it has decreased 1 cm as the total decrease is 2 cm. The lelvel of the candle comes down at half