1. Formula for capillary rise

For a capillary tube of radius $r$, the upward force due to surface tension balances the weight of the liquid column:

$2\pi r\,\sigma \cos\theta = \pi r^2 h \,\rho g$

So,

$h = \frac{2\sigma \cos\theta}{\rho g r}$

where:

• $\sigma$ = surface tension
• $\theta$ = contact angle
• $\rho$ = density of water
• $g$ = acceleration due to gravity
• $r$ = radius of capillary tube

2. Check option A

From

$h = \frac{2\sigma \cos\theta}{\rho g r}$

we see that

$h \propto \frac{1}{r}$

Hence, if $r$ increases, $h$ decreases.

✅ Option A is true.

3. Check option B

Again from the formula,

$h \propto \sigma$

So $h$ depends directly on surface tension and is not independent of $\sigma$.

❌ Option B is false.

4. Check option C

If the lift is going up with constant acceleration $a$, then in the lift frame the effective gravity becomes

$g_{\text{eff}} = g + a$

Thus,

$h = \frac{2\sigma \cos\theta}{\rho r (g+a)}$

Since $g+a > g$, the height $h$ decreases.

✅ Option C is true.

5. Check option D

From the formula,

$h \propto \cos\theta$

not $\theta$ itself.

So $h$ is not proportional to contact angle $\theta$.

❌ Option D is false.

6. Final answer

The correct statements are:

$\boxed{A,\ C}$

7. Comparison with stored correct answer

Stored correct answer: $A, C$

My derived answer matches the stored correct answer.