JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Elasticity & SHM

The elongation of a wire on the surface of the earth is

1 0^{- 4}

m. The same wire of same dimensions is elongated by

6 \times 1 0^{- 5}

m on another planet. The acceleration due to gravity on the planet will be ____ m/s². (Take acceleration due to gravity on the surface of earth = 10 m/s²)

Answer: 6

Solution

For a wire under its own weight, elongation

Δ ℓ \propto g

(since stress

\propto

weight

\propto g

). Therefore,

\frac{Δ ℓ _{earth}}{Δ ℓ _{planet}} = \frac{g _{earth}}{g _{planet}}

. Substituting:

\frac{1 0 ^{- 4}}{6 \times 1 0 ^{- 5}} = \frac{10}{g _{planet}}

, giving

g_{planet} = 10 \times \frac{6 \times 1 0 ^{- 5}}{1 0 ^{- 4}} = 10 \times 0.6 = 6

m/s².

JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Integer answer

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