Physics - Gravitation Question with Solution | TestHub

Given mass density $P=\{P_0$ for $r\le RO$ for $r>R\}$ Since gravitational depends on mass, which is zero for $r>R$, hence it only acts for $r\le R$. $\begin{array}{rl}& {\overrightarrow{\mathrm{F}}}_{\text{graw }}={\overrightarrow{\mathrm{F}}}_{\text{circular }}\\ & \Rightarrow \frac{{\mathrm{GM}}_{\text{sphere }}\times \mathrm{M}}{{\mathrm{R}}^2}=\frac{\mathrm{M}(\mathrm{e}{)}^2}{\mathrm{R}}\\ & \Rightarrow {\mathrm{V}}^2\alpha \frac{{\mathrm{M}}_{\text{sphere }}}{\mathrm{R}}\text{ since }\mathrm{r}\le \mathrm{R}\\ & \Rightarrow {\mathrm{V}}^2\alpha \frac{{\mathrm{R}}^3}{\mathrm{R}}\alpha {\mathrm{R}}^2\Rightarrow \mathrm{V}\alpha \mathrm{R}\text{ straight line }+\mathrm{ve}\text{ slope }\end{array}$ Beyond $\mathrm{r}=\mathrm{R}$, mass density $=0\Rightarrow$ acceleration due to gravity $=0\Rightarrow$ velocity stays constant.