Question 82 of 223

In the reported figure of earth, the value of acceleration due to gravity is same at point $A$ and $C$ but it is smaller than that of its value at point $B$ (surface of the earth). The value of $OA:AB$ will be $x:5$. The value of $x$ is

Your answerCheck answer

Show answer and solution▾

Answer: 4

${g}_{A}=\dfrac{GM\left(r\right)}{{R}^{3}}$
${g}_{C}=\dfrac{GM}{{\left(R+\dfrac{R}{2}\right)}^{2}}$
${g}_{A}={g}_{C}$
$\dfrac{r}{{R}^{3}}=\dfrac{1}{\dfrac{9}{4}{R}^{2}}\Rightarrow r=\dfrac{4R}{9}$
so $OA=\dfrac{4R}{9};AB=R-r=\dfrac{5R}{9}$
$OA:AB=4:5$