Question

Three masses of $500g,300g$ and $100g$ are suspended at the end of a spring as shown in the figure above and are in equilibrium. When the $500g$ mass is removed, the system, oscillates with a period of $2$ second. When the $300g$ mass is also removed, it will oscillate with a period of :

• A. $2s$
• B. $4s$
• C. $8s$
• D. $1s$

Answer 1

The correct option is D $1s$

In one case, net weight = 400g for which let time period be $T$,

whereas on removing 300g more, net weight = 100g, let the new time period be $T^{{}^{\prime }}$.

So, we have ;

$T=2\pi \sqrt{\frac{400}{k}},T^{\prime }=2\pi \sqrt{\frac{100}{k}}$
$\therefore \frac{T^{\prime }}{T}=\sqrt{\frac{100}{400}}=\frac{1}{2}\Rightarrow T^{\prime }=\frac{T}{2}=\frac{2}{2}=1s$