Question

The speed of a transverse wave along a uniform metal wire, when it is under a tension of 1000 g wt is 68 m/s. If the density of metal is 7900 kg/m³, find the area of cross section of the wire. (Ans : 0.2683 mm²)

Answer 1

GIVEN :

T = 1000 g wt. = 1000 × 10⁻³ kg wt.

= 1 × 9.8 N = 9.8 N

v = 68 m/s

ρ = 7900 kg/m³

v = √T/ m

Since mass of the wire, M = Vρ = Alρ

Also, m = M/ l = Al ρ/l

∴ m = Aρ  

Now,v =√ T/ m

v = √T /Aρ  

∴ v ² = T /Aρ  

∴ A = T/ v ² ρ A = 9.8/ 68 x7900  

∴ A = 2.683 × 10⁻⁷m2

Answer 2

Answer:

GIVEN :

T = 1000 g wt. = 1000 × 10⁻³ kg wt.

= 1 × 9.8 N = 9.8 N

v = 68 m/s

ρ = 7900 kg/m³

v = √T/ m

Since mass of the wire, M = Vρ = Alρ

Also, m = M/ l = Al ρ/l

∴ m = Aρ  

Now,v =√ T/ m

v = √T /Aρ  

∴ v ² = T /Aρ  

∴ A = T/ v ² ρ A = 9.8/ 68 x7900  

∴ A = 2.683 × 10⁻⁷m2

ANSWER

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