A wire of length L and radius r is clamped at one end. On stretching the other end of the wire with a force F, the increase in its length is 1. If another wire of same material but of length 2L and radius 2r is stretched with a force 2F, the increase in its leagth will be

Options

A. 1
B. 2 1
C. `1/2`
D. 4 1

Answer

A

Explanation

`F=kX,(F_(1))/(F_(2))=(k_(1)X_(1))/(k_(2)X_(2))or,(X_(2))/(X_(1))=(k_(1)F_(2))/(k_(2)F_(1))or,(X_(2))/(X_(1))=(A_(1)F_(2)l_(2))/(l_(1)A_(2)F_(1))=(A*2F*2l)/(4A*l*F)=1`
`X_(2)=X_(1)=l`