Question

A body of mass $40\mathrm{kg}$ is resting on a rough horizontal surface and is subjected to a force $P$, which is just enough to start the motion of the body. If ${\mu }_s=5,{\mu }_k=0.4,\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$ and the force $P$ is continuously applied on the body, then the acceleration of the body is

• (A) zero
• (B) 1 m/s²
• (C) 2 m/s²
• (D) 2.4 m/s²

Answer 1

The Correct Option is B

Explanation:
Force $P=f_m={\mu }_s$ mg (when body is rest)When the body starts moving with acceleration a then$$\begin{array}{rl}P-f_k& =ma\\ {\mu }_{s}mg-{\mu }_{k}mg& =ma\\ a& =({\mu }_s-{\mu }_k)g\\ & =(05-0.4)10\\ & =0.1\times 10\mathrm{m}/{\mathrm{s}}^2=1\mathrm{m}/{\mathrm{s}}^2\end{array}$$