A small block of mass 'm' is placed on a plank of mass 'M'. The block is connected to plank with the help of a light string passing over a light smooth pulley as shown in figure. The co-efficient of static friction between the block and plank is `mu`.

The co-efficient of friction between the plank and the horizontal surface is zero. What maximum horizontal force F applied on the block of mass m can make the block and plank not to slide relatively?

Explanation

The forces are shown in figure taking the ground as reference frame.
`N_(2)=mg " " ...(1)`
`F-T-f=0" " ...(2)`
`N_(1)=N_(2)+Mg " " ...(3)`
`T-f=0" "...(4)`
Again, `f_("max")=muN_(2)`
i.e. `f_("max")=mu mg " " ...(5)`
For .m. not to slide relatively on .M.,
`f le f_("max") " " ...(6)`
Using equation (1) to (5) and the condition (6), `F_("max") ` can be found out as,
`F_("max")=2mu mg`.