Question

Water $(\rho =1000{\text{kg/m}}^3)$ and kerosene $(\rho =800{\text{kg/m}}^3)$ are filled separately in two identical cylindrical vessels having small heights. Both vessels have small holes at their bottom. The speed of the water and kerosene coming out of their holes are $v_1$ and $v_2$ respectively. Select the correct option.

• A. $v_1=v_2$
• B. $v_1=3v_2$
• C. $v_1=2v_2$
• D. $v_1=4v_2$

Answer 1

The correct option is A $v_1=v_2$

Given,
Speed of water $(\rho =1000{\text{kg/m}}^3)$ coming out of hole $=v_1$
Speed of kerosene $(\rho =800{\text{kg/m}}^3)$ coming out of hole $=v_2$
We know that for small heights of vessels, speed of efflux is independent of density of fluid.
Speed of efflux for small holes, $v=\sqrt{2gh}$ which is independent of density.


Therefore, $v_1=v_2$