A block of mass M rests on a rough horizontal surface as shown. Coefficient of friction between the block and the surface is mu. A force F=mg acting at angle theta with the vertical side of the block pulls it. In which of the following cases the block can be pulled along the surface?

A block of mass M rests on a rough horizontal surface as shown. Coeffi

1.	A block of mass M rests on a rough horizontal surface as shown. Coefficient of friction between the block and the surface is mu. A force F=mg acting at angle theta with the vertical side of the block pulls it. In which of the following cases the block can be pulled along the surface?
Answer» `tan theta ge mu` `tan ((theta)/(2) ge mu)` `cos theta ge mu` `cot ((theta)/(2)) ge mu` Solution :(d) `N=Mg-F cos theta` `=Mg-Mg cos theta=2 Mg sin^(2)"" (theta)/(2)` Further block can be PULLED if, `F sin theta ge mu N cos theta` `implies "" 2Mg sin""(theta)/(2).cos""( theta)/(2) ge 2 mu Mg sin^(2)""(theta)/(2) implies cot""(theta)/(2) ge mu`