Gravitation

JEE Main level, numerical answer, medium

34 of 223

Question 34 of 223

The elongation of a wire on the surface of the earth is 10−4m{10}^{-4}m. The same wire of same dimensions is elongated by 6×10−5m6\times {10}^{-5}m on another planet. The acceleration due to gravity on the planet will be _____ ms−2m{s}^{-2}. (Take acceleration due to gravity on the surface of earth =10ms−2=10{ms}^{-2})

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Answer: 6

Change in length ∝\proptoForce∝mg\propto mg
mg=kx=(YAl)xmg=kx=\left(\dfrac{YA}{l}\right)x
Thus, x∝gx\propto g
Then, 10−46×10−5=gg′⇒g′=0.6g=6ms−2\dfrac{{10}^{-4}}{6\times {10}^{-5}}=\dfrac{g}{{g}^{'}}\Rightarrow {g}^{'}=0.6g=6m{s}^{-2}

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