1
JEE Main 2023 (Online) 31st January Morning Shift
+4
-1

If 1000 droplets of water of surface tension $$0.07 \mathrm{~N} / \mathrm{m}$$, having same radius $$1 \mathrm{~mm}$$ each, combine to from a single drop. In the process the released surface energy is :-

$$\left( {\mathrm{Take}\,\pi = {{22} \over 7}} \right)$$

A
$$7 .92 \times 10^{-4} \mathrm{~J}$$
B
$$7 .92 \times 10^{-6} \mathrm{~J}$$
C
$$8 .8 \times 10^{-5} \mathrm{~J}$$
D
$$9 .68 \times 10^{-4} \mathrm{~J}$$
2
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
A force is applied to a steel wire 'A', rigidly clamped at one end. As a result elongation in the wire is $0.2 \mathrm{~mm}$. If same force is applied to another steel wire ' $\mathrm{B}$ ' of double the length and a diameter $2.4$ times that of the wire ' $\mathrm{A}$ ', the elongation in the wire ' $\mathrm{B}$ ' will be (wires having uniform circular cross sections)
A
$6 .9 \times 10^{-2} \mathrm{~mm}$
B
$6.06 \times 10^{-2} \mathrm{~mm}$
C
$2.77 \times 10^{-2} \mathrm{~mm}$
D
$3.0 \times 10^{-2} \mathrm{~mm}$
3
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, $$5 \mathrm{~cm}$$. If the tube is dipped in a similar manner in another liquid $$\mathrm{B}$$ of surface tension and density double the values of liquid $$\mathrm{A}$$, the height of liquid column raised in liquid $$\mathrm{B}$$ would be __________ m.

A
0.05
B
0.20
C
0.5
D
0.10
4
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1

Choose the correct relationship between Poisson ratio $$(\sigma)$$, bulk modulus (K) and modulus of rigidity $$(\eta)$$ of a given solid object :

A
$$\sigma=\frac{3 K+2 \eta}{6 K+2 \eta}$$
B
$$\sigma=\frac{3 K-2 \eta}{6 K+2 \eta}$$
C
$$\sigma=\frac{6 K+2 \eta}{3 K-2 \eta}$$
D
$$\sigma=\frac{6 K-2 \eta}{3 K-2 \eta}$$
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