Question

7.A planet has a mass of eight times the mass of the earth and density is also equal to 8 times the average density o f the earth.If 'g' be the acceleration due to earths gravity on its surface,then acceleration due to gravity on planets surface will be

Answer 1

$$\begin{gathered} Densityofplanet=8\times densityofearth \\ {D}_p=8\times D_e \\ massoftheplanet=8\times massoftheearth \\ {M}_p=8\times M_e \\ Since \\ {D}_p=8\times D_e \\ \frac{M_p}{{\displaystyle \frac{4}{3}{{\mathrm{\pi R}}_{\mathrm{p}}}^3}}=8\times \frac{M_e}{{\displaystyle \frac{4}{3}{{\mathrm{\pi R}}_e}^3}} \\ {R}_p=R_e \\ thereforetheirradiusissame. \\ \frac{g_p}{g_e}=\frac{{\displaystyle \frac{G{M}_p}{{R_p}^2}}}{\frac{G{M}_e}{{R_e}^2}}=\frac{8M_e}{M_e} \\ {g}_p=8g_e \end{gathered}$$