Question

A horizontal force, just sufficient to move a body of mass $4\text{kg}$ lying on a rough horizontal surface, is applied on it. The coefficient of static and kinetic friction between the body and the surface are 0.8 and 0.6, respectively. If the force continues to act even after the block has started moving, the acceleration of the block in ${\text{m/s}}^2$ is $(g=10{\text{m/s}}^2)$

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $2$
• D. $4$

Answer 1

The correct option is C $2$

The minimum force required to just move a body will be $f_1=\mu mg$. After the motion is started, the friction will become kinectic. So the force which is responsible for the increase in the velocity of the block is
$F=({\mu }_s-{\mu }_k)mg$
$=(0.8-0.6)\times 4\times 10=8\text{N}$
So, $a=\frac{F}{m}=\frac{8}{4}=2{\text{m/s}}^2$