Question

A block of mass $m$ collides with a horizontal weightlessness spring of force constant $k$. The block compresses the spring by $x$. Calculate the maximum momentum of the block. All surfaces are smooth.

• A. $\left(\sqrt{3km}\right)x$
• B. $\left(\sqrt{km}\right)x$
• C. $\left(\sqrt{5km}\right)x$
• D. $\left(\sqrt{7km}\right)x$

Answer 1

The correct option is B $\left(\sqrt{km}\right)x$

Here,

After the compression in the spring,

Potential energy stored$=\frac{1}{2}k{x}^2$

This will be converted to Kinetic energy of the mass $m$,

And at the instant of conversion, momentum will be maximum,

$\frac{1}{2}m{v}^2=\frac{p^2}{2m}=\frac{1}{2}k{x}^2$

$p^2=km{x}^2$

$p=\left(\sqrt{km}\right)x$

Option $\text{B}$ is the correct answer