Question

A force of ${10}^3$ newton stretches the length of a hanging wire by 1 millimetre. The force required to stretch a wire of same material and length but having four times the diameter by 1 millimetre is

• A. $4\times {10}^{3}N$
• B. $16\times {10}^{3}N$
• C. $\frac{1}{4}\times {10}^{3}N$
• D. $\frac{1}{16}\times {10}^{3}N$

Answer 1

The correct option is B $16\times {10}^{3}N$

(c) $F=Y\times A\times \frac{l}{L}\Rightarrow F\propto r^2$
(Y,l and L are constant)
If diameter is made four times then force required will be 16 times.i.e $16\times {10}^{3}N$