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 Evening Shift
+4
-1

The area of cross section of the rope used to lift a load by a crane is $$2.5 \times 10^{-4} \mathrm{~m}^{2}$$. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be :

(take $$g=10 \,m s^{-2}$$ )

A
$$6.25\times 10^{-4} \mathrm{~m}^{2}$$
B
$$10\times 10^{-4} \mathrm{~m}^{2}$$
C
$$1\times 10^{-4} \mathrm{~m}^{2}$$
D
$$1.67\times 10^{-4} \mathrm{~m}^{2}$$
3
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
$$5.3 \times 10^{-4} \mathrm{~J}$$
4
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
$$\frac{3}{20 \sqrt{(2 \rho-\sigma)}}$$
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