Question

A block of mass ${}^{\prime }{m}^{\prime }$ is pulled by horizontal constant force $F=5\mu mg$ over a rough surface of coefficient of friction $\mu$ as shown. Initially spring was at its natural length, the position where block will finally comes to rest will be

• A. $\frac{\mu mg}{k}$
• B. $\frac{4\mu mg}{k}$
• C. $\frac{6\mu mg}{k}$
• D. $\frac{8\mu mg}{k}$

Answer 1

The correct option is B $\frac{4\mu mg}{k}$

Block will return after maximum elongation
i.e $F.x_{max}-1/2K{x}_{max}^2-\mu mg{x}_{max}=0$

$x_{max}=\frac{2(F-\mu mg)}{k}=\frac{8\mu mg}{k}$
So block will finally comes to rest returning i.e. $v=0$ & $a=0$.
By work energy theorem while returning
$-(\frac{1}{2}k{x}^2-\frac{1}{2}k{x}_{max}^2)-(F+\mu mg)(x_{max}-x)=0\Rightarrow x=\frac{4\mu mg}{k}$