1.

A mass of 2.5 kg is hung on a steel wire. This increases 0.25 cm in its length. Determine the work done to pull the wire. (g = 10 m/s2) [Hint: Mg = kx, W = \(\frac{1}{2}\) kx2]

Answer»

Given; F = 2.5 xg = 2.5 × 10 = 25 N
x = 0.25 cm = 0.25 x 10-2 m = 2.5 x 10-3 m
If the force constant of the wire be k, then
\(F=k x \Rightarrow k=\frac{F}{x}=\frac{25}{2.5 \times 10^{-3}}=10^{4} \mathrm{N} \cdot \mathrm{m}^{-1}\)

∴ The work done in pulling the wire,
W = \(\frac{1}{2}\) kx2= \(\frac{1}{2}\) × 104 × 2.5 x 2.5 x 10-6
= \(\frac{1}{2}\)× 6.25 × 10-2
= 3.125 x 10-2 J = 0.03125 J


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