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. $\frac{F}{\sqrt{m K}}$
• B. $\frac{F}{2 \sqrt{m K}}$
• C. $\frac{F}{\sqrt{2 m K}}$
• D. $\frac{2 F}{\sqrt{m K}}$

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
$-\frac{1}{2} \, K \, \left(\frac{F}{K}\right)^{2}+F\left(\frac{F}{K}\right)=\frac{1}{2}mv_{m a x}^{2}$
$\frac{F^{2}}{2 K}=\frac{1}{2}mv_{m a x}^{2}$
$v_{m a x}=\frac{F}{\sqrt{m K}}$