A block of mass `1kg` is pushed against a rough vertical wall with a force of `20N`, coefficient of static friction being `(1)/(4)` Another horizontal force of `10N` is applied on the block in a direction parallel to the wall. Will the block move? If yes, in which direction ? If no, find the frictional force exerted by the wall on the block. `(g = 10m//s^(2))`

Explanation

Normal reaction on the block from the wall will be
N=F=20 N

Therefore, limiting friction
`f_(L)=mu N=((1)/(4))(20)=5N`
Weight of the block is
W=mg=(1)(10)=10N
A horizontal force of 10 N is applid to the block. The resultant of these two forces will be `10sqrt(2)`N in the direction shown in figure. Since, this resultant is greatere than the limiting friction. The block will move in the direction of `F_("net")` with acceleration :

`a=(F_("net")=f_(L))/(m)=(10sqrt(2)-5)/(1)=9.14 ms ^(-2)`