1
JEE Main 2023 (Online) 31st January Evening Shift
+4
-1
For a solid rod, the Young's modulus of elasticity is $3.2 \times 10^{11} \mathrm{Nm}^{-2}$ and density is $8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$. The velocity of longitudinal wave in the rod will be.
A
$3.65 \times 10^3 \mathrm{~ms}^{-1}$
B
$6.32 \times 10^3 \mathrm{~ms}^{-1}$
C
$18.96 \times 10^3 \mathrm{~ms}^{-1}$
D
$145.75 \times 10^3 \mathrm{~ms}^{-1}$
2
JEE Main 2023 (Online) 31st January Evening Shift
+4
-1
Under the same load, wire A having length $5.0 \mathrm{~m}$ and cross section $2.5 \times 10^{-5} \mathrm{~m}^{2}$ stretches uniformly by the same amount as another wire B of length $6.0 \mathrm{~m}$ and a cross section of $3.0 \times 10^{-5}$ $\mathrm{m}^{2}$ stretches. The ratio of the Young's modulus of wire A to that of wire $B$ will be :
A
$1: 2$
B
$1: 4$
C
$1: 1$
D
$1: 10$
3
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
$$9 .68 \times 10^{-4} \mathrm{~J}$$
4
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
$3.0 \times 10^{-2} \mathrm{~mm}$
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