Student Login

Home›Chapters›Mechanical Properties of Solids PYQs›Elastic Potential Energy›Question 9

JEE Main 2020 (9 Jan, Shift 2) · Elastic Potential Energy

Elastic Potential Energy question from JEE Main 2020 (9 Jan, Shift 2)

Q9JEE Main 2020 · 9 JAN · SHIFT 2Medium

Elastic Potential Energy

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1: 4, the ratio of their diameters is:

Show answer and solution

Answer: (d)

$u = \dfrac{S^2}{2Y}$ with $S = \dfrac{F}{\pi d^2/4}$ , so for the same load and material $u \propto \dfrac{1}{d^4}$ .
$\dfrac{u_1}{u_2} = \left(\dfrac{d_2}{d_1}\right)^4 = \dfrac{1}{4}$
$\dfrac{d_1}{d_2} = 4^{1/4} = \sqrt{2}$
So the answer is (d) $\sqrt{2} : 1$ .

Report a mistake

More questions on Elastic Potential Energy

A wire of length ' L ' and area of cross section ' A ' is made of material of Young's…MHT CET 2019 (2 May, Shift 2)
When a block of mass M is suspended by a long wire of length L, the length of the wire…NEET 2019
Work done in stretching a wire through 1 mm is 2 J. What amount of work will be done for…MHT CET 2019 (2 May, Shift 1)
A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of…JEE Main 2019 (8 Apr, Shift 1)
If S is stress and Y is young's modulus of material of a wire, the energy stored in the…JEE Main 2005 (AIEEE)
A wire fixed at the upper end stretches by length l by applying a force F. The work done…JEE Main 2004 (AIEEE)
A wire suspended vertically from one of its ends is stretched by attaching a weight of…JEE Main 2003 (AIEEE)
A copper wire of length 3 m is stretched by 3 mm by applying an external force. The…JEE Main 2026 (5 Apr, Shift 2)