question_answer

A solid sphere is made to roll down from the same height on two inclined planes having different angles of inclination. In which case will it take less time to reach the bottom?

Answer:

                As two inclined planes have different inclinations, but same height, therefore, velocity on reaching the bottom along two inclines is the same. From     \[\upsilon =u+at=0+at\] \[t=\upsilon /a\] Now, \[\upsilon \]is same and \[a\propto \sin \theta \] \[\therefore \]  \[t\propto \frac{1}{\sin \theta }\] i.e. time taken will be smaller when the rolls down the plane of higher inclination.