The height of a liquid in a fine capillary tube(a) Increases with an increase in the density of a liquid(b) Decreases with a decrease in the diameter of the tube(c) Decreases with an increase in the surface tension(d) Increases as the effective value of acceleration due to gravity isdecreased

The height of a liquid in a capillary tube is determined by several factors:

(a) Increases with an increase in the density of a liquid: This statement is incorrect. The height of a liquid in a capillary tube decreases with an increase in the density of the liquid. This is because the denser the liquid, the more mass it has, and the more force gravity exerts on it, pulling it down and reducing the height it can reach in the capillary tube.

(b) Decreases with a decrease in the diameter of the tube: This statement is correct. The height of a liquid in a capillary tube decreases as the diameter of the tube decreases. This is due to the increased surface tension in a narrower tube, which pulls the liquid down and reduces the height it can reach.

(c) Decreases with an increase in the surface tension: This statement is incorrect. The height of a liquid in a capillary tube increases with an increase in surface tension. Surface tension is the force that causes the liquid to "stick" to the sides of the tube and climb upwards. The greater the surface tension, the higher the liquid can climb.

(d) Increases as the effective value of acceleration due to gravity is decreased: This statement is correct. The height of a liquid in a capillary tube increases as the effective value of acceleration due to gravity decreases. This is because gravity pulls the liquid down, so a decrease in gravity allows the liquid to climb higher in the tube.