Water rises in a vertical capillary tube upto a height of 2.0 cm. If the tube is inclined at an

step 1 My question is water rises in a vertical capillary tube up to 8, up to a height of 2 cm. If the

Water rises in a vertical capillary tube upto a height of...

Water rises in a vertical capillary tube upto a height of $2.0 \mathrm{~cm}$. If the tube is inclined at an angle of $60^{\circ}$ with the vertical, then upto what length the water will rise in the tube (a) $2.0 \mathrm{~cm}$ (b) $4.0 \mathrm{~cm}$ (c) $\frac{4}{\sqrt{3}} \mathrm{~cm}$ (d) $2 \sqrt{2} \mathrm{~cm}$

Water rises in a vertical capillary tube upto a height of $2.0 \mathrm{~cm}$. If the tube is inclined at an angle of $60^{\circ}$ with the vertical, then upto what length the water will rise in the tube
(a) $2.0 \mathrm{~cm}$
(b) $4.0 \mathrm{~cm}$
(c) $\frac{4}{\sqrt{3}} \mathrm{~cm}$
(d) $2 \sqrt{2} \mathrm{~cm}$

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Key Concepts

Capillary Action

Capillary action refers to the phenomenon where a liquid spontaneously rises or falls in a narrow tube due to the adhesive forces between the liquid and the tube walls, in conjunction with the cohesive forces within the liquid. This effect is commonly observed in thin tubes and is a consequence of the balance between surface tension and gravitational pull.

Geometric Resolution in Inclined Tubes

In problems involving inclined capillary tubes, the vertical height reached by the liquid is the projection of the actual length of the liquid column along the tube on the vertical axis. This requires resolving the column length into its vertical component using trigonometric principles.

Trigonometric Relationships

Trigonometry, especially the cosine function, is fundamental in relating the angle of the tube's inclination to the effective vertical height of the liquid column. When a tube is inclined, the vertical height is calculated by multiplying the length of the liquid column by the cosine of the angle between the tube and the vertical.

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