Physics - SHM Question with Solution | TestHub

It is given that, acceleration due to gravity on planet $A$ is 9 times the acceleration due to gravity on planet $B$ ie, $$g_A=9g_B$$ From third equation of motion $$v^2=2gh$$ At planet $A,h_A=\frac{v^2}{2g_A}$ At planet $B,h_B=\frac{v^2}{2g_B}$ Dividing Eq. (ii) by Eq. (iii), we have $$\frac{h_A}{h_B}=\frac{g_B}{g_A}$$ From Eq. (i), $g_A=9g_B$ $$\frac{h_A}{h_B}=\frac{g_B}{9g_B}=\frac{1}{9}$$ or $h_B=9h_A=9\times 2=18\mathrm{m}\left(\because h_A=2\mathrm{m}\right)$