A container of large uniform cross sectional area A resting on a horizontal surface holds two immiscible non-viscous and incompressible liquids of density d and 3d each of height H/2. The lower density liquid is open to the atmosphere having pressure `P_o`. A tiny hole of area a `(a lt lt A)` is punched on the vertical side of the lower container at a height `h (0 lt h lt H/2)` for which range is maximum.

Options

A. h=H/3
B. Range R=2H/3
C. Range R=3H/2
D. velocity of efflux r `v=sqrt(2/3 gH)`

Explanation

To solve the problem, we need to find the height \( h \) at which the hole is punched in the lower liquid so that the range of the liquid that exits the hole is maximized.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two immiscible liquids in a container. The lower liquid has density \( d \) and the upper liquid has density \( 3d \).
- Both liquids have a height of \( \frac{H}{2} \).
- The lower liquid is open to the atmosphere at pressure \( P_0 \).
...