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A solid copper sphere of radius ‘r’ is suspended from a point using a steel wire of length ‘l’ and radius ‘r’. The elongation in the steel wire is 1 mm. If that sphere is replaced with another copper sphere of radius ‘2r’ the elongation in that steel wire would be _______ mm.

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answer is 8.

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Detailed Solution

$Δ ℓ \propto M = \frac{4}{2} π R^{3} ρ$

$\frac{Δ ℓ_{2}}{Δ ℓ_{1}} = {(\frac{R_{2}}{R_{1}})}^{3} = 8$

$Δ ℓ_{2} = 8 \times 1 = 8 m m$

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