The elongation of a wire on the surface of the earth is 10 - 4 m. The same wire of same dimensions is elongated by 6 \times 10 - 5 m on another planet. The acceleration due to gravity on the planet will be \underline\hspace2cm ms - 2. (Take acceleration due to gravity on the surface of earth = 10 ms - 2)

Properties of Matter PYQ — JEE Main 2022 · 26 Jun · Shift 1 · Q62 with Solution

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Correct answer: 6

For a wire stretched by a load,

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

where:

So,

\Delta L \propto F \propto g

for the same wire and same mass/load.

Hence,

\frac{\Delta L_p}{\Delta L_e} = \frac{g_p}{g_e}

On Earth:

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

On the planet:

\Delta L_p = 6 \times 10^{-5}\,\text{m}

Also,

g_e = 10\,\text{m s}^{-2}

Therefore,

g_p = g_e \cdot \frac{\Delta L_p}{\Delta L_e}

g_p = 10 \cdot \frac{6 \times 10^{-5}}{10^{-4}}

\frac{6 \times 10^{-5}}{10^{-4}} = 6 \times 10^{-1} = 0.6

So,

g_p = 10 \times 0.6 = 6\,\text{m s}^{-2}

\boxed{6}