Question 303: Properties of Matter

Question

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 $$	imes$$ 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
)

Accepted Answer

on earth, $$\Delta l = {10^{ - 4}}\,m$$
on other planet $$\Delta l' = 6 	imes {10^{ - 5}}\,m$$
$$\Delta l = {{Fl} \over {Ay}} \Rightarrow {{\Delta l'} \over {\Delta l}} = {{{{F'l} \over {Ay}}} \over {{{Fl} \over {Ay}}}} = {{mg'} \over {mg}}$$
$$ \Rightarrow g' = {{\Delta l'} \over {\Delta l}} 	imes g$$
$$ = {{6 	imes {{10}^{ - 5}}} \over {{{10}^{ - 4}}}} 	imes 10$$
$$ \Rightarrow g' = 6$$ m/s
2

Properties of Matter

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 )

Integer / Numeric Answer Type