A solid copper sphere of radius r elongates a fixed steel suspension wire by 1 mm. It is replaced by a copper sphere of radius 2r. Find the new elongation (mm) of the same wire.
Physics · Mixed Chapter
JEE Main Practice

Question

A solid copper sphere of radius r elongates a fixed steel suspension wire by 1 mm. It is replaced by a copper sphere of radius 2r. Find the new elongation (mm) of the same wire.

G1 Physics · Accepted Answer

Step 1: Wire extension Δℓ=FL/(YA); L, Y and A are unchanged. Step 2: The weight of equal-density solid spheres scales with volume ∝r³. Step 3: Doubling radius multiplies weight by 2³=8. Step 4: New extension =8×1=8 mm.