A) AGP
B) AP
C) GP
D) HP
Correct Answer: D
Solution :
Since, \[{{R}_{1}}\] and \[{{R}_{2}}\] respectively be the maximum ranges up and down an inclined plane, then \[{{R}_{1}}=\frac{{{u}^{2}}}{g(1+\sin \beta )}\] \[{{R}_{2}}=\frac{{{u}^{2}}}{g(1-\sin \beta )}\] \[R=\frac{{{u}^{2}}}{g}\] Now, \[\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}=\frac{g(1+\sin \beta )}{{{u}^{2}}}+\frac{g(1-\sin \beta )}{{{u}^{2}}}\] \[=\frac{g(1+\sin \beta +1-\sin \beta )}{{{u}^{2}}}\] \[=\frac{2g}{{{u}^{2}}}=\frac{2}{R}\] \[\Rightarrow \] \[\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}=\frac{2}{R}\] \[\Rightarrow \] \[\frac{1}{{{R}_{1}}},\frac{1}{R},\frac{1}{{{R}_{2}}}\] are in AP. \[\Rightarrow \] \[{{R}_{1}},R,{{R}_{2}}\] are in HP.
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