Question

Three masses $0.1\text{kg},0.3\text{kg}$ and $0.4\text{kg}$ are suspended at end of a spring. When the $0.4\text{kg}$ mass is removed, the system oscillates with a period $2\text{s}$. When the $0.3\text{kg}$ mass is also removed, the system will oscillate with a period

• A. $1\text{s}$
• B. $2\text{s}$
• C. $3\text{s}$
• D. $4\text{s}$

Answer 1

The correct option is A $1\text{s}$

Total mass suspended at the end of spring $\left(M\right)=m_1+m_2+m_3$
$=0.1+0.3+0.4$
$=0.8\text{kg}$
Given that, when $0.4\text{kg}$ mass is removed, net mass of the system is $0.4\text{kg}$ the system oscillates with a period $\left(T_1\right)$ of $2\text{s}$.

If $0.3\text{kg}$ mass is also removed, Net mass of the system is $0.1\text{kg}$, let time period of oscillation is $T_2$


$\frac{T_2}{T_1}=\sqrt{\frac{m_2}{m_1}}=\sqrt{\frac{0.1}{0.4}}=\frac{1}{2}$

$T_2=\frac{1}{2}\times 2=1\text{s}$