A block rests on a rough plane whose inclination ( ) to the horizontal can be varied. Which of the following graphs indicates how the frictional force (F ) between the block and the plane varies as ( ) is increased ?

Step-by-step solution

For a resting block, static friction equals ( mg ) up the plane until the limiting value ( mg ) is reached at ( = ); hence F rises with ( ) initially. Beyond this angle, the block cannot remain at rest and static friction cannot increase further, so the graph must peak and then drop as motion sets in. This qualitative behavior matches option (b).