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? A. `tan theta ge mu`B. `tan ((theta)/(2) ge mu)`C. `cos theta ge mu`D. `cot ((theta)/(2)) ge mu`

Answer» Correct Answer - D
(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`


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