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7.Gravitation
medium
Find the gravitational field at a distance of $2000\, km$ from centre of earth. (in $m / s ^{2}$)
(Given $\left.R_{\text {earth }}=6400 km , r =2000 km , M _{\text {earth }}=6 \times 10^{24} kg \right)$
A
$1.53$
B
$7.12$
C
$3.06$
D
$1.8$
(AIIMS-2019)
Solution
The expression for gravitational force at some distance from surface is given by,
$g^{\prime}=\frac{G M}{R^{3}} r$
$=\frac{G M}{R^{2}} \cdot \frac{r}{R}$
$=g \frac{r}{R}$ $….(I)$
Substitute $9.8 m / s ^{2}$ for $g, 2000\, m$ for $r$ and $6400\, m$ for $R$ in equation $(I).$
$g^{\prime}=9.8 \times \frac{2000}{6400}$
$=3.06 m / s ^{2}$
Standard 11
Physics
