Question

A disc of mass $3m$ and a disc of mass $m$ are connected by a massless spring of stiffness $k$.The heavier disc is placed on the ground with the spring vertical and lighter disc on top. From its equilibrium position the upper disc is pushed down by a distance $\delta$ and released.Then

• A. if $\delta >\frac{3mg}{k}$, the lower disc will bounce up
• B. if $\delta >\frac{2mg}{k}$, maximum normal reaction from ground on lower $disc=6mg$
• C. if $\delta >\frac{2mg}{k}$, maximum normal reaction from ground on lower $disc=4mg$
• D. if $\delta >\frac{4mg}{k}$, the lower disc will bounce up

Answer 1

Answer: (B), (D)

The correct options are
B if $\delta >\frac{2mg}{k}$, maximum normal reaction from ground on lower $disc=6mg$
D if $\delta >\frac{4mg}{k}$, the lower disc will bounce up

$\left(a\right)\text{At equilibrium}$
$k{\delta }_0=mg\text{or}{\delta }_0=\frac{mg}{k}$
$\text{where}{\delta }_0=\text{compression}$
$\left(b\right){\delta }_{Total}=\delta +{\delta }_0=\frac{3mg}{k}$
$F_{max}=k{\delta }_{max}=k\left(\frac{3mg}{k}\right)=3mg$
$\therefore N_{max}=3mg+F_{max}=6mg$