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Question: Two wires A and B have the same length and area of cross section. But Young’s modulus of A is two ti...

Two wires A and B have the same length and area of cross section. But Young’s modulus of A is two times the Young’s modulus of B. Then the ratio of force constant of A to that of B is

A

1

B

2

C

12\frac{1}{2}

D

2\sqrt{2}

Answer

2

Explanation

Solution

Force constant of wire k=YALk = \frac{YA}{L} ⇒ kAkB=YAYB=2\frac{\mathbf{k}_{\mathbf{A}}}{\mathbf{k}_{\mathbf{B}}}\mathbf{=}\frac{\mathbf{Y}_{\mathbf{A}}}{\mathbf{Y}_{\mathbf{B}}}\mathbf{= 2}

[As L and A are same]