A) \[\frac{\sqrt{2}}{3}{{\tan }^{-1}}\sqrt{2}+\frac{5}{12}\,\log \,2-\frac{1}{4}\,\log \,3\]
B) \[\frac{\sqrt{2}}{3}{{\tan }^{-1}}\sqrt{2}-\frac{5}{12}\,\log \,2-\frac{1}{12}\,\log \,3\]
C) \[\frac{\sqrt{2}}{3}{{\tan }^{-1}}\sqrt{2}+\frac{5}{12}\,\log \,2+\frac{1}{4}\,\log \,3\]
D) \[\frac{\sqrt{2}}{3}{{\tan }^{-1}}\sqrt{2}-\frac{5}{12}\,\log \,2+\frac{1}{\sqrt{12}}\,\log \,3\]
Correct Answer: D
Solution :
Let \[u=v,\] \[u=v+at\] \[0=v-at\] \[\therefore \] \[-a=\frac{0-v}{t}=-\frac{v}{t}\] \[f=\mu R=\mu mg\] (resolved in partially) \[a=\mu g\] \[\therefore \] \[t=\frac{v}{a}=\frac{v}{g\mu }\] \[\eta =\frac{{{P}_{0}}}{{{P}_{i}}}\] \[\therefore \] \[\frac{1}{2}\,m{{v}^{2}}=16\,\,J\] \[v=4\,m{{s}^{-1}}\] \[Mg\,\,\sin \,\,\theta \] \[Mg\,\,\sin \theta \times \frac{h}{2}Mg\,\cos \,\theta \,\times r\]
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