A block of mass $m$ placed on a rough horizontal plane is pulled by a constant power $P$. The coefficient of friction between the block and the surface is $\mu$. The maximum velocity of the block will be

• A

  $\frac{\mu P}{m g}$
• B

  $\frac{\mu \mathrm{mg}}{P}$
• C

  $\mu m g P$
• Correct answer
  D

  $\frac{P}{\mu m g}$

Solution

The given situation is as shown below
Here, $N=m g$ and $f r_k=\mu N=\mu m g$ $\begin{aligned} & \because \quad \text { Power, } P=F v \cos \left(0^{\circ}\right)=F v \times 1=F v \\ & \quad v=\frac{P}{F}=\frac{P}{f r_k} \\ & \quad v_{\max }=\frac{P}{\left(f r_k\right)_{\min }}(\text { as } P=\text { constant }) \Rightarrow v_{\max }=\frac{P}{\mu m g} \end{aligned}$

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