1
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

Potential energy as a function of r is given by $$U = {A \over {{r^{10}}}} - {B \over {{r^5}}}$$, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

A
$${\left( {{A \over B}} \right)^{{1 \over 5}}}$$
B
$${\left( {{B \over A}} \right)^{{1 \over 5}}}$$
C
$${\left( {{2A \over B}} \right)^{{1 \over 5}}}$$
D
$${\left( {{B \over 2A}} \right)^{{1 \over 5}}}$$
2
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

The bulk modulus of a liquid is 3 $$\times$$ 1010 Nm$$-$$2. The pressure required to reduce the volume of liquid by 2% is :

A
3 $$\times$$ 108 Nm$$-$$2
B
9 $$\times$$ 108 Nm$$-$$2
C
6 $$\times$$ 108 Nm$$-$$2
D
12 $$\times$$ 108 Nm$$-$$2
3
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $$\times$$ 103 kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 $$\times$$ 1011 Pa, g = 9.8 m/s2]
A
3.60 $$\times$$ 10$$-$$8
B
2.60 $$\times$$ 10$$-$$7
C
1.87 $$\times$$ 10$$-$$3
D
7.07 $$\times$$ 10$$-$$4
4
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
A uniform heavy rod of weight 10 kg ms$$-$$2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 $$\times$$ 1011 Nm$$-$$2. Neglecting the lateral contraction, find the elongation of rod due to its own weight.
A
2 $$\times$$ 10$$-$$9 m
B
5 $$\times$$ 10$$-$$8 m
C
4 $$\times$$ 10$$-$$8 m
D
5 $$\times$$ 10$$-$$10 m
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