1
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7.3 $$\times$$ 10$$-$$2 Nm$$-$$1, angle of contact = 0, g = 10 ms2 and density of water = 1.0 $$\times$$ 103 kg m$$-$$3]
A
3.62 mm
B
2.19 mm
C
5.34 mm
D
4.97 mm
2
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is :

[Density of water fw = 1000 kg m$$-$$3 and Density of air fa = 1.2 kg m$$-$$3, g = 10 m/s2, Coefficient of viscosity of air = 1.8 $$\times$$ 10$$-$$5 Nsm$$-$$2]
A
250.6 ms$$-$$1
B
43.56 ms$$-$$1
C
4.94 ms$$-$$1
D
14.4 ms$$-$$1
3
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a < < A) :

A
$${A \over {2a}}$$
B
None of these
C
$${{2a} \over A}$$
D
$${{a} \over A}$$
4
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Two series of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y1 and Y2. The combination behaves as a single wire then its Young's modulus is :
A
$$Y = {{2{Y_1}{Y_2}} \over {3({Y_1} + {Y_2})}}$$
B
$$Y = {{2{Y_1}{Y_2}} \over {{Y_1} + {Y_2}}}$$
C
$$Y = {{{Y_1}{Y_2}} \over {2({Y_1} + {Y_2})}}$$
D
$$Y = {{{Y_1}{Y_2}} \over {{Y_1} + {Y_2}}}$$
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