JEE MAIN - Physics (2022 - 26th June Morning Shift - No. 21)
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 ____________ ms$$-$$2. (Take acceleration due to gravity on the surface of earth = 10 ms$$-$$2)
Answer
6
Explanation
on earth, $$\Delta l = {10^{ - 4}}\,m$$
on other planet $$\Delta l' = 6 \times {10^{ - 5}}\,m$$
$$\Delta l = {{Fl} \over {Ay}} \Rightarrow {{\Delta l'} \over {\Delta l}} = {{{{F'l} \over {Ay}}} \over {{{Fl} \over {Ay}}}} = {{mg'} \over {mg}}$$
$$ \Rightarrow g' = {{\Delta l'} \over {\Delta l}} \times g$$
$$ = {{6 \times {{10}^{ - 5}}} \over {{{10}^{ - 4}}}} \times 10$$
$$ \Rightarrow g' = 6$$ m/s2
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