A horizontal force just sufficient to move a body of mass $4 \mathrm{~kg}$ lying on a rough horizontal surface, is applied on it. Coefficients of static and kinetic frictions are 0.8 and 0.6 respectively. If the force continues to act even after the body has started moving, the acceleration of the body is $\left(\right.$ take, $g=10 \mathrm{~ms}^{-2}$ ).

• A

  $6 ms^{-2}$
• B

  $8 ms^{-2}$
• Correct answer
  C

  $2 ms^{-2}$
• D

  $4 ms^{-2}$

Solution

Initially
$\begin{aligned} & F=f_s=\mu_s N \\ & =0.4 \times 4 \times 10=32 \mathrm{~N}\end{aligned}$ Finally,
$\begin{aligned} & \mathrm{F}-\mathrm{f}_{\mathrm{k}}=\mathrm{ma} \\ & 32-\mu_{\mathrm{k}} \mathrm{mg}=\mathrm{ma} \\ & \Rightarrow \quad 32-0.6 \times 40=4 \mathrm{a} \\ & \Rightarrow \quad 8=4 \mathrm{a} \\ & \Rightarrow \mathrm{a}=2 \mathrm{~m} / \mathrm{s}^2\end{aligned}$

Hence, the correct answer is option: 'C'.