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7.Gravitation
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A uniform spherical planet (Radius $R$) has acceleration due to gravity at its surface $g.$ Points $P$ and $Q$ located inside and outside the planet have acceleration due to gravity $\frac{g}{4} .$ Maximum possible separation between $P$ and $Q$ is
A
$\frac{{7R}}{4}$
B
$\frac{{3R}}{4}$
C
$\frac{{9R}}{4}$
D
none
Solution
variation with depth
$g_{d}=g(1-d / R)$
$\frac{g}{4}=g(1-d / R)$
$\frac{d}{R}=3 / 4$
$a=3 R / 4$
variation with height
$g_{h}=g\left(1-\frac{2 h}{R}\right)$
$\frac{g}{4}=g\left(1-\frac{2 h}{R}\right)$
$\frac{2 h}{R}=\frac{3}{4}$
$h=\frac{3 R}{8}$
max distance $=a+h=\frac{3 R}{4}+\frac{3 R}{8}$
$=\frac{9 R}{8}$
Standard 11
Physics
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