The elongation of a steel wire stretched by a force is 'e'. If a wire of the same material of double the length, and half the diameter is subjected to double the force, its elongation will be

Options

A. 16e
B. 4e
C. `e/4`
D. `e/16`

Answer

A

Explanation

`(F_(1)l_(1))/(r_(1)^(2)Deltal_(1)) = (F_(2)l_(2))/(r_(2)^(2)Deltal_(2))` [`because` The material sis same, E is same]
`(F_(1)l_(1))/(r^(2)e) = ((2F_(1))(2l_(1)))/((r/2)^(2)Deltal_(2))`
`therefore Delta l_(2) = 16e`