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 × 10^-5 m on another planet. The acceleration due to gravity on the planet will be _______ ms^-2.

(Take acceleration due to gravity on the surface of earth = 10 ms^-2)

Concept:  

Elongation of the length of wire can be as:

\(Δ L = \frac{FL}{AE}\)    -----(1)

Where F = force on object, L = length of object, E = Modulus of elasticity, A = area of object

Where F = Mg then Equation (1) can be written as:

\(Δ L = \frac{MgL}{AE}\)  which shows ΔL∝ g      -----(2) 

Calculation:

Given: 

Elongation of wire on the surface of the earth (ΔL₁)= 10^-4 m 

On another planet elongation of the same wire is (ΔL₂) = 6 × 10^-5 m

Acceleration due to gravity on the surface of earth = 10 ms-2

Using equation (2) we can write as: \( \frac{Δ L_{1}}{Δ L_{2}} = \frac{g_{earth}}{g_{planet}} \)    -----(3)

Using equation (3) we get:  \(\frac{10^{-4}}{6 \times 10^{-5}} = \frac{10}{g_{planet}}\) by solving we get  g_planet = 6 m/s²

Hence, the value of acceleration due to gravity on another planet is = 6 m/s2