A wire has a breaking stress of 6 × 105 N / m 2 and a density of 3 × 104 kg / m 3. The length of the wire of the same material which will break under its own weight, (if g=10 m / s 2 ) is

Question

A wire has a breaking stress of 6 × 105 N / m 2 and a density of 3 × 104 kg / m 3. The length of the wire of the same material which will break under its own weight, (if g=10 m / s 2 ) is (A) 2000 m (B) 2500 m (C) 20 m (D) 2 m

Tardigrade Admin · Accepted Answer

Breaking stress is given by =6 × 105 N / m 2=(m g/A) (But m=A L ρ ) 6 × 105=(A L ρ g/A)=L ρ g Thus, L=(6 × 105/ρ g)=(6 × 105/3 × 104 × 10)=2 m

Q. A wire has a breaking stress of $6 \times 1 0^{5} N / m^{2}$ and a density of $3 \times 1 0^{4} k g / m^{3}$ . The length of the wire of the same material which will break under its own weight, (if $g = 10 m / s^{2}$ ) is

2000 m

2500 m

20 m

2 m

Breaking stress is given by
$= 6 \times 1 0^{5} N / m^{2} = \frac{m g}{A}$
(But $m = A L ρ$ )
$6 \times 1 0^{5} = \frac{A L ρ g}{A} = L ρ g$
Thus, $L = \frac{6 \times 1 0 ^{5}}{ρ g} = \frac{6 \times 1 0 ^{5}}{3 \times 1 0 ^{4} \times 10} = 2 m$

Q. A wire has a breaking stress of 6×105N/m2 and a density of 3×104kg/m3. The length of the wire of the same material which will break under its own weight, (if g=10m/s2 ) is

2000 m

2500 m

20 m

2 m

Breaking stress is given by =6×105N/m2=Amg​ (But m=ALρ ) 6×105=AALρg​=Lρg Thus, L=ρg6×105​=3×104×106×105​=2m

Q. A wire has a breaking stress of $6 \times 1 0^{5} N / m^{2}$ and a density of $3 \times 1 0^{4} k g / m^{3}$ . The length of the wire of the same material which will break under its own weight, (if $g = 10 m / s^{2}$ ) is

Breaking stress is given by
$= 6 \times 1 0^{5} N / m^{2} = \frac{m g}{A}$
(But $m = A L ρ$ )
$6 \times 1 0^{5} = \frac{A L ρ g}{A} = L ρ g$
Thus, $L = \frac{6 \times 1 0 ^{5}}{ρ g} = \frac{6 \times 1 0 ^{5}}{3 \times 1 0 ^{4} \times 10} = 2 m$