A block is kept on a rough horizontal surface. The acceleration of the block increases from $6 \mathrm{~ms}^{-2}$ to $11 \mathrm{~ms}^{-2}$ when the horizontal force acting on it increases from 20 N to 30 N . The coefficient of kinetic friction between the block and the surface is (Acceleration due to gravity $=10$ $\mathrm{ms}^{-2}$ )

• A

  0.2
• B

  0.3
• Correct answer
  C

  0.4
• D

  0.5

Solution

Acceleration of the block, $\mathrm{a}=\frac{\mathrm{F}-\mathrm{fi}}{\mathrm{m}}=\frac{\mathrm{F}-\mu \mathrm{img}}{\mathrm{m}}$

$\therefore a_1=\frac{F_1-\mu m g}{m} \Rightarrow \sigma=\frac{20-\mu m g}{m}$...(i) Also, $a_2=\frac{F_2-\mu \mathrm{mg}}{\mathrm{m}} \Rightarrow 11=\frac{30-\mu \mathrm{mg}}{\mathrm{m}}$..(ii) From eq (i) and (ii), we get $\frac{6}{11}=\frac{20-\mu \mathrm{mg}}{30-\mu \mathrm{mg}} \Rightarrow \mu=\frac{8}{\mathrm{mg}}=\frac{8}{\left(\frac{30-20}{11-6}\right) \times 10}=0.4$

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