1
JEE Main 2023 (Online) 8th April Morning Shift
+4
-1 An air bubble of volume $$1 \mathrm{~cm}^{3}$$ rises from the bottom of a lake $$40 \mathrm{~m}$$ deep to the surface at a temperature of $$12^{\circ} \mathrm{C}$$. The atmospheric pressure is $$1 \times 10^{5} \mathrm{~Pa}$$ the density of water is $$1000 \mathrm{~kg} / \mathrm{m}^{3}$$ and $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$$. There is no difference of the temperature of water at the depth of $$40 \mathrm{~m}$$ and on the surface. The volume of air bubble when it reaches the surface will be:

A
$$4 \mathrm{~cm}^{3}$$
B
$$3 \mathrm{~cm}^{3}$$
C
$$2 \mathrm{~cm}^{3}$$
D
$$5 \mathrm{~cm}^{3}$$
2
JEE Main 2023 (Online) 8th April Morning Shift
+4
-1 An aluminium rod with Young's modulus $$Y=7.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$$ undergoes elastic strain of $$0.04 \%$$. The energy per unit volume stored in the rod in SI unit is:

A
5600
B
2800
C
11200
D
8400
3
JEE Main 2023 (Online) 6th April Evening Shift
+4
-1 Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$

Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed.

Reason R: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.

In the light of the above statements, choose the most appropriate answer from the options given below

A
Both A and R are correct but R is NOT the correct explanation of A
B
A is not correct but R is correct
C
A is correct but R is not correct
D
Both A and B are correct and R is the correct explanation of A
4
JEE Main 2023 (Online) 6th April Morning Shift
+4
-1 A small ball of mass $$\mathrm{M}$$ and density $$\rho$$ is dropped in a viscous liquid of density $$\rho_{0}$$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?

A
$$\mathrm{F}=\mathrm{Mg}\left(1-\frac{\rho_{\mathrm{O}}}{\rho}\right)$$
B
$$\mathrm{F}=\mathrm{Mg}\left(1+\frac{\rho}{P_{o}}\right)$$
C
$$\mathrm{F}=\mathrm{Mg}\left(1+\frac{\rho_{\mathrm{o}}}{\rho}\right)$$
D
$$F=M g\left(1 \pm \rho \rho_{0}\right)$$
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