Question

A wire of lenght L and Radius r is clamped rigidly at one end when the other end of the wire is pulled by a force it's lengthy increases by L another wire of the same material of the length 2L and radius 2R is pulled by a force 2F find the increase in length of this wire?​

Answer 1

Answer:

Correct option is

C

l

Let Y be Young's modulus of the material of the wire, Then for the first wire

Y=

l/L

F/πr

2

=

πr

2

l

FL

...(i)

As both the wires are made of the same material, so their

Young modulus is same

Let the extension produced in second wire be l

′

. Then

Y=

l

′

/2L

2F/π(2r)

2

=

πr

2

l

′

FL

...(ii)

Equating (i) and (ii) ,we get

πr

2

l

FL

=

πr

2

l

′

FL

orl

′

=l