A box of mass $50\text{kg}$ is kept on horizontal floor. When it is pushed by a horizontal force $F,$ it moves with constant velocity. If it is pushed by a horizontal force $1.5F,$ it moves with constant acceleration of $0.1{\text{m/s}}^2$. Find the value of $F.$

The correct option is A $10\text{N}$
Case 1:
Body moves with constant velocity. Hence, force of kinetic friction $\left(f\right)$ should be balanced by applied force $\left(F\right).$
$\Rightarrow F=f$

Case 2:
Applied force is increased to $1.5F$.

Using Newton's Second Law of Motion,
$1.5F-f=ma$
$\Rightarrow 1.5F-F=ma$
$\Rightarrow 0.5F=50\times 0.1$
$\Rightarrow F=10\text{N}$