Answer :
Final Answer:
The mass (m) of the water that rises in the capillary tube of radius (r) can be determined using the capillary rise equation:[tex]\( m = \pi r^2 h \rho \), where \( h \) is the height of the capillary rise and \( \rho \) is the density of water.[/tex]
Explanation:
The capillary rise in a tube is influenced by the surface tension of the liquid (water, in this case) and the geometry of the tube. The mass of the water that rises ( m ) can be calculated using the formula [tex]\( m = \pi r^2 h \rho \),[/tex]
- ( pi ) is a mathematical constant (approximately 3.14),
- ( r ) is the radius of the capillary tube,
- ( h ) is the height of the capillary rise,
- ( p) is the density of water.
This formula is derived from the balance between the upward force due to surface tension and the downward force due to gravity. The surface area of the cross-section of the capillary tube[tex](\( \pi r^2 \))[/tex]he height of the capillary rise h gives the volume of water lifted. Multiplying this by the density of water[tex](\( \rho \))[/tex]ss.
Understanding and applying this formula allows for the precise calculation of the mass of water rising in a capillary tube based on its radius, the capillary rise, and the density of water.
