Question

The Young's modulus of brass and steel are respectively 1.0 × 10¹¹ Nm^-2 and 2.0 × 10¹¹ Nm^-2. A brass wire and a steel wire of the same length are extended by 1 mm each under the same force. If the radii of brass and steel wire are R_B and R_S respectively, then ______.

पर्याय

• `R_S = sqrt2R_B`

• `R_S = R_B/sqrt2`

• `R_S = 4R_B`

• `R_S = R_B/2`

Answer 1

The Young's modulus of brass and steel are respectively 1.0 × 10¹¹ Nm^-2 and 2.0 × 10¹¹ Nm^-2. A brass wire and a steel wire of the same length are extended by 1 mm each under the same force. If the radii of brass and steel wire are R_B and R_S respectively, then `underlinebb(R_S = R_B/sqrt2)`.

Explanation:

Increase in length, ΔL = `(FL)/(YA) = (FL)/(YpiR^2)`

As, F, L and ΔL are the same, hence YR² = constant.

∴ `2.0 xx 10^11 R_S^2 = 1.0 xx 10^11 R_B^2`

⇒ `R_s = R_B/sqrt2`