question_answer

A solid wooden sphere rolls down two different inclined planes of the same height but of different inclinations. (a) Will it reach the bottom with same speed in each case? (b) Will it take longer to roll down one inclined plane than other? Explain.

Answer:

                (a) Yes, because speed at the bottom depends only on height and not on slope.                 (b) Yes, greater the inclination \[(\text{ }\!\!\theta\!\!\text{ })\], smaller will be the time of descent, as \[t\propto 1/\sin \text{ }\!\!\theta\!\!\text{ }\].