Question

A body of mass 40kg resting on rough horizontal surface is subjected to a force '$P$ ' which is just enough to start the motion of the body. If ${\mu }_s=0.5,{\mu }_k=0.4,g=10m/s^2$ and the force '$P$ ' is continuously applied on the body, then the acceleration of the body is

• A. Zero
• B. $1m/s^2$
• C. $2m/s^2$
• D. $2.4m/s^2$

Answer 1

Answer: (B)

$1m/s^2$

Since $P$ is the force which is just enough to start the motion of the body,

$P={\mu }_{s}N={\mu }_{s}mg$

When the body moves under this force, the net force on body is given by

$F=ma=P-f$
$⟹ma={\mu }_{s}mg-{\mu }_{k}N$
$=m({\mu }_s-{\mu }_k)g$

$⟹a=({\mu }_s-{\mu }_k)g$

$=(0.5-0.4)\left(10\right)m/s^2$

$⟹a=1m/s^2$