A long U-tube contains mercury (density = 14×103 kg/m3). When 10cm of water (density =1 .0 ×103 kg/m3) is poured into the left arm, the mercury in the right arm rises above its original level by

A long U-tube contains mercury (density = 14 × 103 kg/m^3). When 10 cm of water (density = 1.0 × 103 kg/m^3) is poured into the left arm, the mercury in the right arm rises above its original level by:  

A. 0.36 cm  B. 0.72 cm  C. 14 cm  D. 35 cm  

Option B is the right choice as the rise in the mercury level is of 0.72 cm.

Explanation:

Given:

Density of the mercury, =  

Density of the water, =

Water poured on the left arm of the U-tube, =

According to the question:

The mercury in the right arm rises above its original.

We have to find this rise, .

Lets  take a horizontal reference line on the U-tube.

Note:

In a static fluid there is no horizontal variation of pressure.

So,

Considering = on left and right of the manometer.

Hydro-static pressure =

⇒

⇒

⇒ Equating both.

⇒

⇒

⇒

⇒ Plugging the values.

⇒

⇒

⇒ cm ≈ cm

So the rise of the mercury in the right arm is of 0.72 cm.

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