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7.Gravitation
medium
પૃથ્વીની સપાટીથી $1\; km$ ઊંચાઇએ ગુરુત્વપ્રવેગ પૃથ્વીની સપાટીથી $d$ ઊંડાઇએ ગુરુત્વપ્રવેગ જેટલો છે, તો ઊંડાઈ $d\,=$ ......... $km$
A
$\frac{4}{3}$
B
$\;\frac{3}{2}$
C
$\;\frac{2}{3}$
D
$2$
(NEET-2017)
Solution
The acceleration due to gravity at a height $h$ is given as
${g_h} = g\left( {1 – \frac{{2h}}{{{R_e}}}} \right)$
Where $R_e$ is radius of earth.
The acceleration due to gravity at a depth $d$ is given as
${g_d} = g\left( {1 – \frac{d}{{{R_e}}}} \right)$
Given, ${g_h} = {g_d}$
$g\left( {1 – \frac{{2h}}{{{R_e}}}} \right) = g\left( {1 – \frac{d}{{{R_e}}}} \right)$
$d = 2h = 2 \times 1 = 2km\left( {h = 1\,km} \right)$
Standard 11
Physics
