NEET 2020 Physics Question 178 Solution

When a capillary tube of internal radius $$r$$ is immersed in water, the meniscus forms a contact angle $$\theta$$. Surface tension $$T$$ acts along the contact perimeter $$2\pi r$$. The upward vertical force supporting the liquid column is: $$F_{\text{up}} = 2\pi r T \cos\theta$$.

At equilibrium, this upward force balances the weight of the liquid inside the capillary: $$W = m g$$ $$m g = 2\pi r T \cos\theta \implies m = \frac{2\pi r T \cos\theta}{g}$$.

Since surface tension $$T$$, contact angle $$\theta$$, and $$g$$ are constant for the water-glass system: $$m \propto r$$ (Note: Even though height $$h = \frac{2T\cos\theta}{\rho g r} \propto \frac{1}{r}$$ halves, the cross-sectional area $$A = \pi r^2$$ quadruples, so volume $$V = A h \propto r^2 \times (1/r) = r$$, confirming $$m \propto r$$).

For the second tube with radius $$r_2 = 2r$$: $$m_2 = 2 \times m_1 = 2 \times 5\text{ g} = 10.0\text{ g}$$. Matches Option 3.