JEE Main20204 Sep 2020Evening ShiftPhysicsMechanical Properties of FluidsActual
Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d . The area of the base of both vessels is S but the height of liquid in one vessel is x 1 and in the other x 2 . When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in e
Options
- Ag d S x 2 2 + x 1 2
- Bg d S x 2 + x 1 2
- C3 4 g d S x 2 - x 1 2
- D1 4 g d S x 2 - x 1 2
Correct answer
D. 1 4 g d S x 2 - x 1 2
Step-by-step solution
Initial height of liquid in container's of same cross section are x 1 and x 2 respectively. Now value is opened find loss in potential energy when water level be become same loss in PE = U i - U f = ρ ( A ) x 1 x 1 2 + ρAx 2 x 2 2 g - ρA x 1 + x 2 2 × x 1 + x 2 4 × 2 g = ρAg x 1 2 2 + x 2 2 2 - x 1 + x 1 2 4 = ρAg x 1 - x 2 2 4