Question

2
The Young's modulus of brass and steel are 1 x 10' N/m and 2 x 10' N/m
respectively. If wires of both materials, having same length, are loaded with same
weight, then they both extend by 4 mm. Ratio of the radii of two wires Rg :Rs is​

Answer 1

Answer:

The Young’s modulus of brass and steel are respectively 1.0 × 1010 N/m2 and 2 × 1010 N/m2. A brass wire and a steel wire of the same length are extended by 1 mm under the same force, the radii of brass and steel wires are RB and RS respectively. Then

Answer

RS = 2√ RB

Answer 2

answer : √2 : 1

we know, Young's modulus = stress/strain

⇒Y = F/πr²(∆l/l)

⇒Y ∝ 1/r²

here it is clear that Young's modulus is inversely proportional to square of radius of wire.

given, Young's modulus of brass, Y_g = 1 × 10¹¹ N/m²

Young's modulus of steel, Y_s = 2 × 10¹¹ N/m²

so, 1 × 10¹¹/2 × 10¹¹ = (R_s/R_g)²

⇒R_s/R_g = 1/√2

⇒R_g/R_s = √2

hence, ratio of radii of brass to steel wire is √2 : 1

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