Two wires of the same length and same material but radii in the ratio of `1:2` are stretched by unequal forces to produce equal elongation. The ratio of the two forces is

Options

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

Answer

D

Explanation

(d) Given, `r_(1)=r, r_(2)=2r`
Now, we know that, `Y=(F)/(A)*(l)/(Deltal)=(F)/(pir^(2))*(l)/(Deltal)`
So, `(F)/(pir_(1)^(2))=(f)/(pir_(2)^(2)) " "[because l, Deltal " and " Y ` are same]
`(F)/(f)=(r_(1)^(2))/(r_(2)^(2))implies (F)/(f)=(r^(2))/(4r^(2))implies(F)/(f)=(1)/(4)`