The U-tube in the figure is sealed at both ends.It contains a gas in A,another gas in B,and mercury in C.The heights of the mercury in the two arms are as shown.The density of mercury is 13.6 g/cm³.If the pressure in A is 1 $\times$ 10⁴ dyn/cm²,the pressure in B is A)1 $\times$ 10⁴ dyn/cm² B)2 $\times$ 10⁴ dyn/cm² C)3 $\times$ 10⁴ dyn/cm² D)4 $\times$ 10⁴ dyn/cm² E)5 $\times$ 10⁴ dyn/cm²

Question

Quizplus · Accepted Answer

We know that the pressure at any point in a fluid is given by:

pressure = density x gravity x height

In arm A, the pressure is given to be 1 x 10^10 dyn/cm^2. Let the height of gas A be h1.

In arm B, the pressure is given by P = 13.6 x 980 x h2, where h2 is the height of gas B.

Since the U-tube is sealed, the pressure at the same height in both arms must be the same. Therefore:

1 x 10^10 = 13.6 x 980 x h2 + 13.6 x 980 x (h2 + 13) + 13.6 x 980 x 76

Solving for h2, we get h2 = 2 cm.

Therefore, the pressure in gas B is given by:

P = 13.6 x 980 x 2 = 2 x 10^5 dyn/cm^2.

Hence, the answer is (B).

The U-Tube in the Figure Is Sealed at Both Ends ×\times×

The U-Tube in the Figure Is Sealed at Both Ends $\times$