Question

A massless spring of length $l$ and spring constant $k$ is placed vertically on a table. A all of mass m is just kept on top of the spring. The maximum velocity of the ball is

• A. $g \sqrt{\frac{m}{k}}$
• B. $g \sqrt{\frac{2m}{k}}$
• C. $2g \sqrt{\frac{m}{k}}$
• D. $\frac{g}{2} \sqrt{\frac{m}{k}}$

Answer 1

Answer: (A)

$g \sqrt{\frac{m}{k}}$

Answer 2

If $x=$ displacement of free end of spring, then
$m g=k x$
or $X=\frac{m g}{k}$
Time period of oscillation, $T=2 \pi \sqrt{\frac{m}{k}}$
$\Rightarrow \omega=$ Angular frequency
$=\frac{2 \pi}{T}=\sqrt{\frac{k}{m}}$
Maximum velocity of oscillating mass
$=V_{\max }=A \omega$
$=\frac{m g}{k} \times \sqrt{\frac{k}{m}} =g \sqrt{\frac{m}{k}}$