Q131 / 160 · TS EAMCET 2024 (10 May Shift 2) · Physics
The ratio of the radii of a planet and the earth is $1: 2$, the ratio of their mean densities is $4: 1$. If the acceleration due to gravity on the surface of the earth is $9.8 \mathrm{~ms}^{-2}$, then the acceleration due to gravity on the surface of the planet is
- A$4.9 \mathrm{~ms}^{-2}$
- B$8.9 \mathrm{~ms}^{-2}$
- C$29.4 \mathrm{~ms}^{-2}$
- Correct answerD$19.6 \mathrm{~ms}^{-2}$
Solution
For plant and earth,
$\begin{aligned} & r_1: r_2=1: 2, \delta_1: \delta_2=4: 1, g_2=9.8 \mathrm{~ms}^{-2} \\ & \therefore \text { Acceleration due to gravity, } g=\frac{4}{3} \pi \delta \mathrm{Gr} \\ & \therefore \mathrm{g} \propto \delta \mathrm{r} \\ & \therefore \frac{\mathrm{g}_1}{\mathrm{~g}_2}=\frac{\delta_1}{\delta_2} \cdot \frac{\mathrm{q}_1}{\mathrm{r}_2}=\frac{4}{1} \times \frac{1}{2}=2 \\ & \therefore \mathrm{gl}=2 \mathrm{~g} 2=2 \times 9.8=19.6 \mathrm{~ms}-2\end{aligned}$
Hence, the correct answer is option: 'D'.