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(D) At the condition of equilibrium,the pressure at the same horizontal level in a continuous liquid is equal.Let the horizontal level be at the botto

Vedclass · Accepted Answer

$9.6$

Vedclass · Answer

(D) At the condition of equilibrium,the pressure at the same horizontal level in a continuous liquid is equal.Let the horizontal level be at the bottom of the glycerin column,passing through points $A$ and $B$ as shown in the diagram.Pressure at point $A$ = Pressure at point $B$.The pressure at $A$ is due to the glycerin column of height $10 	ext{ cm}$.$P_A = h_{	ext{glycerin}} 	imes ho_{	ext{glycerin}} 	imes g = 10 	imes 1.3 	imes g$.The pressure at $B$ is due to the oil column of height $h$ and the mercury column of height $(10 - h)$.$P_B = h 	imes ho_{	ext{oil}} 	imes g + (10 - h) 	imes ho_{	ext{mercury}} 	imes g = h 	imes 0.8 	imes g + (10 - h) 	imes 13.6 	imes g$.Equating $P_A$ and $P_B$:$10 	imes 1.3 	imes g = h 	imes 0.8 	imes g + (10 - h) 	imes 13.6 	imes g$.Dividing by $g$:$13 = 0.8h + 136 - 13.6h$.$13 = 136 - 12.8h$.$12.8h = 136 - 13 = 123$.$h = \frac{123}{12.8} \approx 9.609 	ext{ cm}$.Rounding to the nearest given option,the length of the oil column is $9.6 	ext{ cm}$.

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