Question

Initially, a block of mass $m$ is at rest on a frictionless floor and the spring is in a relaxed condition. One end of the spring is rigidly attached to the block and the other end is fixed to a wall. A constant force is applied on the block as shown in the figure. The maximum velocity of the block is

• A. $\frac{F}{\sqrt{mK}}$
• B. $\frac{F}{2\sqrt{mK}}$
• C. $\frac{F}{\sqrt{2mK}}$
• D. $\frac{2F}{\sqrt{mK}}$

Answer 1

Answer: (A)

The block attains maximum speed when it passes through its equilibrium position.
$F=Kx$
$x=\frac{F}{K}$
From work-energy theorem
$-\frac{1}{2}K{\left(\frac{F}{K}\right)}^2+F\left(\frac{F}{K}\right)=\frac{1}{2}m{v}_{max}^2$
$\frac{F^2}{2K}=\frac{1}{2}m{v}_{max}^2$
$v_{max}=\frac{F}{\sqrt{mK}}$