Question

A block of mass ' $m$ ' is attached to a spring in natural length of spring constant ' $k^{\prime }$. The other end $A$ of the spring is moved with a constant velocity $v$ away from the block. Find the maximum extension in the spring.

• A. $\frac{1}{4}\sqrt{\frac{m{v}^2}{k}}$
• B. $\sqrt{\frac{m{v}^2}{k}}$
• C. $\frac{1}{2}\sqrt{\frac{m{v}^2}{k}}$
• D. $2\sqrt{\frac{m{v}^2}{k}}$

Answer 1

Answer: (B)

Consider an observer moving with speed $v$ with point $A$ in the same direction.

In the frame of observer, block will have initial velocity $v$ towards left.

During maximum extension, the block will come to rest witl respect to the observer. Now, by energy conservation,
$\frac{1}{2}m{v}^2=\frac{1}{2}k{x}_{\max }^2$
$\Rightarrow x_{\max }=\sqrt{\frac{m{v}^2}{k}}.$