A block of mass 1kg is pushed against a rough vertical wall with a force of 20 N, coefficient of static friction being $\frac{1}{4}$Another horizontal force of 10N is applied on the block in a direction parallel to the wall. What will be the acceleration of the block? $\left(g=10 \mathrm{m}/{\mathrm{s}}^2\right)$

  Normal reaction on the block from the wall will be $\left(F_{\text{net }}=0\right.$, perpendicular to the wall)

Therefore, limiting friction

$R=F=20 \mathrm{N}$

Weight of the block is

$w=mg=\left(1\right)\left(10\right)=10 \mathrm{N}$

A horizontal force of $10 \mathrm{N}$ is applied to the block. Both weight and this force are along the wall. The resultant of these two forces will be $10\sqrt{2} \mathrm{N}$ in the direction shown in figure. Since, this resultant is greater than the limiting friction. The block will move in the direction of ${\mathrm{F}}_{\text{net }}$ with acceleration

$a=\frac{{\mathbf{F}}_{\text{net }}-f_L}{m}=\frac{10\sqrt{2}-5}{1}=9.14 \mathrm{m}/{\mathrm{s}}^2$