Question 360: Gravitation

Question

For a body of mass '$$m$$', the acceleration due to gravity at a distance '$$R$$' from the surface of the earth is $$\left(\frac{g}{4}\right)$$. Its value at a distance $$\left(\frac{R}{2}\right)$$ from the surface of the earth is ( $$R=$$ radius of the earth, $$g=$$ acceleration due to gravity)

Accepted Answer

$$\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{r}^2} \quad$$ where $$\mathrm{r}$$ is the distance from the centre of the earth
In the first case, $$r_1=R+R=2 R$$
In the second case, $$r_2=R+\frac{R}{2}=\frac{3}{2} R$$
$$\begin{aligned}
	herefore \frac{g_2}{g_1} & =\left(\frac{r_1}{r_2}ight)^2=\frac{4 	imes 4}{9}=\frac{16}{9} \
g_2 & =\frac{16}{9} g_1=\frac{16}{9} 	imes \frac{9}{4}=\frac{4}{9} g
\end{aligned}$$

Answer

$$\left(\frac{g}{8}\right)$$

Answer

$$\left(\frac{9 g}{4}\right)$$

Answer

$$\left(\frac{4 g}{9}\right)$$

Answer

$$\left(\frac{\mathrm{g}}{2}\right)$$

Gravitation

For a body of mass '$m', the acceleration due to gravity at a distance 'R' from the surface of the earth is \left(\frac{g}{4}\right). Its value at a distance \left(\frac{R}{2}\right) from the surface of the earth is ( R= radius of the earth, g=$ acceleration due to gravity)

Choose the correct answer: