Question

In a uniform U-tube containing water, if a liquid of density \(800\ \mathrm{kg\,m^{-3}}\) is poured into one of its limbs to a height of \(25\) cm, then the rise in water level in the other limb of the tube is

• A. \(25\) cm
• B. \(20\) cm
• C. \(10\) cm
• D. \(40\) cm

Hint:

In a uniform U-tube, if one side rises by \(x\), the other side falls by \(x\). Hence, the pressure balance is \[ \boxed{\rho_1h=\rho_2(2x).} \]

Answer 1

The Correct Option is C

Step 1: Let the rise of water in one limb be \(x\). Since the U-tube is uniform, the water level in the other limb falls by the same amount. Hence, the difference in the water levels is \[ 2x. \]

Step 2: Apply the condition of equal pressure. Pressure due to the liquid column: \[ \rho_1gh = 800\times g\times25. \] Pressure due to the water column: \[ \rho_2g(2x) = 1000\times g\times2x. \] Equating the pressures, \[ 800\times25 = 1000\times2x. \] Therefore, \[ x = \frac{800\times25}{2000} = 10\text{ cm}. \]

Step 3: Write the answer. Hence, the rise of water level in the other limb is \[ \boxed{10\text{ cm}}. \] Thus, \[ \boxed{(C)} \] is the correct answer.