Three masses 100 text{ g}, 300 text{ g}, and | vedclass

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(B) The time period of a spring-mass system is given by $T = 2\pi \sqrt{\frac{m}{k}}$, where $m$ is the mass and $k$ is the spring constant.Initially,

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$1.5$

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(B) The time period of a spring-mass system is given by $T = 2\pi \sqrt{\frac{m}{k}}$, where $m$ is the mass and $k$ is the spring constant.Initially, the masses are $m_1 = 100 	ext{ g}$, $m_2 = 300 	ext{ g}$, and $m_3 = 500 	ext{ g}$.When the $500 	ext{ g}$ mass is removed, the remaining mass is $M_1 = 100 	ext{ g} + 300 	ext{ g} = 400 	ext{ g}$.The period is $T_1 = 3 	ext{ s}$.So, $3 = 2\pi \sqrt{\frac{400}{k}}$.When the $300 	ext{ g}$ mass is also removed, the remaining mass is $M_2 = 100 	ext{ g}$.Let the new period be $T_2$.So, $T_2 = 2\pi \sqrt{\frac{100}{k}}$.Dividing the two equations:$\frac{T_2}{3} = \frac{2\pi \sqrt{100/k}}{2\pi \sqrt{400/k}} = \sqrt{\frac{100}{400}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$.Therefore, $T_2 = 3 	imes \frac{1}{2} = 1.5 	ext{ s}$.

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