A wire of Young's modulus 2×10¹¹ N/m² has longitudinal stress 6×10⁷ N/m². Its volume increases by 0.02%. If fractional decrease of radius is x×10⁻⁵, find x.
Physics · Mixed Chapter
JEE Main Practice

Question

A wire of Young's modulus 2×10¹¹ N/m² has longitudinal stress 6×10⁷ N/m². Its volume increases by 0.02%. If fractional decrease of radius is x×10⁻⁵, find x.

G1 Physics · Accepted Answer

Step 1: Longitudinal strain ε_L =stress/Y=(6×10⁷)/(2×10¹¹)=3×10⁻⁴. Step 2: Fractional volume change ΔV/V = 0.02/100 = 2×10⁻⁴. Step 3: For a cylinder, ΔV/V=ε_L+2ε_r. Thus 2ε_r=2×10⁻⁴−3×10⁻⁴=−1×10⁻⁴. Step 4: ε_r=−5×10⁻⁵. Radius decrease magnitude is 5×10⁻⁵, so x=5.