List - I (Height from the surface of the earth) | List - II (Value of g) |
(a) \[\frac{R}{10}\] | (k) \[\frac{25g}{36}\] |
(b) \[\frac{R}{20}\] | (I) \[\frac{100g}{121}\] |
(c) \[\frac{R}{30}\] | (m) \[\frac{900g}{961}\] |
(d) \[\frac{R}{5}\] | (h) \[\frac{400g}{441}\] |
Answer:
\[g\,\,at\frac{R}{10}\Rightarrow {{g}_{1}}=\frac{g{{R}^{2}}}{{{\left( R+\frac{R}{10} \right)}^{2}}}=\frac{100g}{121}\] \[\Rightarrow g\,\,at\frac{R}{20}\Rightarrow {{g}_{2}}=\frac{g{{R}^{2}}}{{{\left( R+\frac{R}{20} \right)}^{2}}}=\frac{400g}{441}\] \[\Rightarrow g\,\,at\frac{R}{30}\Rightarrow {{g}_{3}}=\frac{g{{R}^{2}}}{{{\left( R+\frac{R}{30} \right)}^{2}}}=\frac{900g}{961}\] \[\Rightarrow g\,\,at\frac{R}{5}\Rightarrow {{g}_{4}}=\frac{g{{R}^{2}}}{{{\left( R+\frac{R}{5} \right)}^{2}}}=\frac{258}{36}\]
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