Use the formula for elongation of a wire

$\Delta L = \frac{FL}{AY}$

where:

• $F$ = भार (tension due to hanging mass)
• $L = 6\,\text{m}$
• $A = 3\,\text{mm}^2 = 3 \times 10^{-6}\,\text{m}^2$
• $Y = 2 \times 10^{11}\,\text{N/m}^2$

Find gravity on the planet

Given planet gravity is one-fourth of earth's gravity:

$g' = \frac{1}{4} \times 10 = 2.5\,\text{m/s}^2$

Find the force due to the hanging block

$F = mg' = 4 \times 2.5 = 10\,\text{N}$

Substitute into elongation formula

$\Delta L = \frac{10 \times 6}{(3 \times 10^{-6})(2 \times 10^{11})}$

$\Delta L = \frac{60}{6 \times 10^5}$

$\Delta L = 10^{-4}\,\text{m}$

Convert into mm and cm

$10^{-4}\,\text{m} = 0.1\,\text{mm} = 0.01\,\text{cm}$

Match with options

The correct option is:

$\boxed{\text{C: }0.1\,\text{mm}}$

Comparison with stored answer

Stored correct answer: C
Derived answer: C
They match.