question_answer

Match the following

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) \[\frac{400g}{441}\]

(a) \[a-l,\text{b}-\text{h},\text{c}-\text{m},\text{d}-\text{k}\] (b) \[a-l,b-h,d-m,c-k\] (c) \[a-h,\text{ }b-l,\text{ }c-m,\text{ }d-k\] (d) \[a-h,b-m,c-l,d-k\]

Answer:

\[g\,\,at\frac{R}{10}\Rightarrow {{g}_{1}}=\frac{g{{R}^{2}}}{{{\left( R+\frac{R}{10} \right)}^{2}}}=\frac{100g}{121}\] \[\Rightarrow g\,\,at\frac{R}{20}\Rightarrow {{g}_{2}}=\frac{g{{R}^{2}}}{{{\left( R+\frac{R}{20} \right)}^{2}}}=\frac{400g}{441}\] \[\Rightarrow g\,\,at\frac{R}{30}\Rightarrow {{g}_{3}}=\frac{g{{R}^{2}}}{{{\left( R+\frac{R}{30} \right)}^{2}}}=\frac{900g}{961}\] \[\Rightarrow g\,\,at\frac{R}{5}\Rightarrow {{g}_{4}}=\frac{g{{R}^{2}}}{{{\left( R+\frac{R}{5} \right)}^{2}}}=\frac{258}{36}\]