Water rises in a vertical capillary tube up to a height of 2.0 cm. If the tube is inclined at an angle of o 60° with the vertical, then upto what length the water will rise in the tube

The correct option is 4.0 cm.

Step-by-step Explanation:

When a capillary tube is kept vertical, the water rises to a vertical height, let's call it $h$. In this problem, the initial vertical height is:
$h=2.0\text{cm}$

When the capillary tube is inclined at an angle $\theta$ with the vertical, the water column rises along the incline such that its vertical height remains unchanged to maintain hydrostatic equilibrium.

Let $L$ be the length of the water column along the inclined tube. The relationship between the vertical height $h$, the length of the water column $L$, and the angle $\theta$ with the vertical is given by:
$h=L\cos \theta$

Rearranging the formula to solve for the length $L$ along the tube:
$L=\frac{h}{\cos \theta }$

Given the values from the problem:
$h=2.0\text{cm}$
$\theta =60°$

Substituting these values into our relation:
$L=\frac{2.0}{\cos (60°)}$

We know that $\cos (60°)=0.5$:
$L=\frac{2.0}{0.5}=4.0\text{cm}$

Therefore, the water will rise to a length of 4.0 cm in the inclined tube.