The vertical arms of U - tube have unequal raidus R and r `( R gt r)` . If a liquid of surface tension T and density `rho` rests in equillibrium inside the U - tube , find the level difference h between the meniscuses in the two arms .

Explanation

To solve the problem of finding the level difference \( h \) between the meniscuses in the two arms of a U-tube with unequal radii \( R \) and \( r \) (where \( R > r \)), we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a U-tube with two vertical arms. The left arm has a radius \( r \) and the right arm has a radius \( R \). A liquid with surface tension \( T \) and density \( \rho \) is in equilibrium inside the U-tube.

2. **Pressure at the Meniscus**:
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