A wire of diameter 1 mm breaks under a tension of 1000 N. Another wire, of same material as that of the first one, but of diameter 2 mm breaks under a tension of

Q: A wire of diameter 1 mm breaks under a tension of 1000 N. Another wire, of same material as that of the first one, but of diameter 2 mm breaks under a tension of

(a) 500 N

(b) 1000 N

(c) 10000 N

(d) 4000 N

Click to See Answer :
Ans: (d)
Sol: Braking Force ∝ Area of Cross Section

$\frac{F_1}{F_2} = (\frac{r_1}{r_2})^2 $

$\frac{1000}{F_2} = (\frac{1}{2})^2 = \frac{1}{4}$

$ F_2 = 4000 N $