Question

A body slides down a smooth inclined plane when released from the top , while another body falls freely from the same point . Which one will strike the ground earlier ?

Answer 1

$$\begin{gathered} \mathrm{Time}\mathrm{of}\mathrm{fall}: \\ \mathrm{T}=\frac{1}{\mathrm{sin\theta }}\sqrt{\frac{2\mathrm{h}}{\mathrm{g}}} \\ \mathrm{h}\mathrm{and}\mathrm{g}\mathrm{are}\mathrm{same}\mathrm{for}\mathrm{both}\mathrm{bodies}. \\ \mathrm{Hence}, \\ \mathrm{T}\mathrm{\alpha }\frac{1}{\sin \mathrm{\theta }} \\ \mathrm{For}\mathrm{a}\mathrm{freely}\mathrm{falling}\mathrm{body},\mathrm{angle}\mathrm{of}\mathrm{inclined}\mathrm{is}\mathrm{equal}\mathrm{to}90\mathrm{degrees},\mathrm{where}\mathrm{as}\mathrm{for}\mathrm{the} \\ \mathrm{inclined}\mathrm{plane},\mathrm{the}\mathrm{angle}\mathrm{is}\mathrm{less}\mathrm{than}90\mathrm{degrees}. \\ \mathrm{As}\mathrm{T}\mathrm{is}\mathrm{inversely}\mathrm{proportional}\mathrm{to}\mathrm{the}\mathrm{angle}, \\ \mathrm{it}\mathrm{can}\mathrm{be}\mathrm{concluded}\mathrm{that}\mathrm{the}\mathrm{freely}\mathrm{falling}\mathrm{body}\mathrm{reaches}\mathrm{the}\mathrm{ground}\mathrm{earlier}. \end{gathered}$$