1
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1 Two cylindrical vessels of equal cross-sectional area $$16 \mathrm{~cm}^{2}$$ contain water upto heights $$100 \mathrm{~cm}$$ and $$150 \mathrm{~cm}$$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take, density of water $$=10^{3} \mathrm{~kg} / \mathrm{m}^{3}$$ and $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$ ] :

A
0.25 J
B
1 J
C
8 J
D
12 J
2
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1 A water drop of radius $$1 \mathrm{~cm}$$ is broken into 729 equal droplets. If surface tension of water is 75 dyne/ $$\mathrm{cm}$$, then the gain in surface energy upto first decimal place will be :

(Given $$\pi=3.14$$ )

A
$$8.5 \times 10^{-4} \mathrm{~J}$$
B
$$8.2 \times 10^{-4} \mathrm{~J}$$
C
$$7.5 \times 10^{-4} \mathrm{~J}$$
D
$$5.3 \times 10^{-4} \mathrm{~J}$$
3
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1 A drop of liquid of density $$\rho$$ is floating half immersed in a liquid of density $${\sigma}$$ and surface tension $$7.5 \times 10^{-4}$$ Ncm$$-$$1. The radius of drop in $$\mathrm{cm}$$ will be :

(g = 10 ms$$-$$2)

A
$$\frac{15}{\sqrt{(2 \rho-\sigma)}}$$
B
$$\frac{15}{\sqrt{(\rho-\sigma)}}$$
C
$$\frac{3}{2 \sqrt{(\rho-\sigma)}}$$
D
$$\frac{3}{20 \sqrt{(2 \rho-\sigma)}}$$
4
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

An air bubble of negligible weight having radius r rises steadily through a solution of density $$\sigma$$ at speed v. The coefficient of viscosity of the solution is given by :

A
$$\eta = {{4r\sigma g} \over {9v}}$$
B
$$\eta = {{2{r^2}\sigma g} \over {9v}}$$
C
$$\eta = {{2\pi {r^2}\sigma g} \over {9v}}$$
D
$$\eta = {{2{r^2}\sigma g} \over {3\pi v}}$$
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