Deformation of Solids: Question 6

Worked solution

Setting up the problem

Hooke’s law states that the force applied to a spring is directly proportional to its extension, within the limit of proportionality: $F = kx$

Before substituting, convert the extension to SI units (metres): $x = 12\text{ cm} = 12\times10^{-2}\text{ m} = 0.12\text{ m}$

Calculating the force

$F = kx = 25 \times 0.12$ $F = 3.0\text{ N}$

Why the other options are wrong

• A ($0.0048\text{ N}$): this comes from inverting the formula and computing $x/k = 0.12/25$ instead of $kx$.
• C ($30\text{ N}$): this comes from misplacing a power of ten in the conversion, treating $12\text{ cm}$ as $1.2\text{ m}$ instead of $0.12\text{ m}$.
• D ($300\text{ N}$): this comes from failing to convert the extension to metres at all, computing $25\times12$.

Final answer

• Force applied $= \boxed{3.0}\text{ N}$, option B.