Question

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

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

Answer 1

The correct option is D $1$ sec

After removing $500g$-

$T=2\pi \sqrt{\frac{m}{K}}=2sec=2\pi \sqrt{\frac{\frac{400}{100}}{K}}=2sec\to \left(1\right)$

Now after removing $300$g also

$\Rightarrow T=2pi\sqrt{\frac{\frac{100}{1000}}{K}}\to \left(2\right)$

From equation $1$ and $2$

$\frac{2}{T}=\frac{\sqrt{400}}{\sqrt{100}}\frac{2}{T}=\frac{20}{10}T=1sec$