Question

For a body on a horizontal surface, coefficients of static and kinetic frictions are $0.4$ and $0.2$, respectively. When the body is in uniform motion on the surface, a horizontal force equal in magnitude to limiting friction is applied on it. The acceleration produced is

• A. $0.4\text{g}$
• B. $0.1\text{g}$
• C. $0.2\text{g}$
• D. $0.6\text{g}$

Answer 1

The correct option is C $0.2\text{g}$

The magnitude of limiting friction $={\mu }_{S}N={\mu }_{S}mg$. This force is applied on the body towards right. Now, kinetic friction ${\mu }_{K}N$ opposes the motion and acts towards left.
$\therefore$ Net force towards right ${\mu }_{S}N-{\mu }_{K}N$
So acceleration produced $=\frac{({\mu }_{S}N-{\mu }_{K}N)}{m}$
$=\frac{({\mu }_S-{\mu }_K)mg}{m}$
$=({\mu }_S-{\mu }_K)g=(0.4-0.2)\text{g}=0.2\text{g}$
Hence, the correct answer is option (c).