A 100 N force stretches the length of a hanging wire by 0.5 mm. The force required to stretch a wire, of the same material and length but having four times the diameter, by 0.5 mm is

Question

A 100 N force stretches the length of a hanging wire by 0.5 mm. The force required to stretch a wire, of the same material and length but having four times the diameter, by 0.5 mm is (A) 100 N (B) 400 N (C) 1200 N (D) 1600 N

Tardigrade Admin · Accepted Answer

As, Y=(F × 4 × 1/π D2 Δ l) In the given problem, F propto D2 . Since, D is increased by a factor of 4 therefore, F is increased by a factor of 16 . So, F will be 100 × 16=1600 N

Q. A $100 N$ force stretches the length of a hanging wire by $0.5 mm$ . The force required to stretch a wire, of the same material and length but having four times the diameter, by $0.5 mm$ is

100 N

400 N

1200 N

1600 N

As, $Y = \frac{F \times 4 \times 1}{π D ^{2} Δ l}$
In the given problem, $F \propto D^{2} .$ Since, $D$ is increased by a factor of 4 therefore, $F$ is increased by a factor of $16.$ So, $F$ will be $100 \times 16 = 1600 N$

Q. A 100N force stretches the length of a hanging wire by 0.5mm. The force required to stretch a wire, of the same material and length but having four times the diameter, by 0.5mm is