When a certain weight is suspended from a long uniform wire, its length increases by 1 cm. If the same weight is suspended from the other wire of the same material and length but having a diameter half of the first one then the increase in length will be

Options

A. 0.5 cm
B. 2cm
C. 4cm
D. 8cm

Answer

C

Explanation

Increase in length is given by,
`l = (FL)/(AY) implies l prop (1)/(r^(2)) ` ( FL and Y are constant)
`(l_(2))/(l_(2)) = ((r_(1))/(r_(2)))^(2) = (2)^(2) =4 `
`implies l_(2) = 4l_(2) =4` cm