Three masses 700,g, 500,g and 400,g are suspe | vedclass

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

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$2$

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(B) The period of oscillation of a spring-mass system is given by $T = 2\pi \sqrt{\frac{m}{k}}$,where $m$ is the oscillating mass and $k$ is the spring constant.Initially,the system has masses $700\,g, 500\,g,$ and $400\,g$. When the $700\,g$ mass is removed,the remaining mass is $m_1 = 500\,g + 400\,g = 900\,g = 0.9\,kg$. The period is $T_1 = 3\,s$.So,$3 = 2\pi \sqrt{\frac{0.9}{k}}$.When the $500\,g$ mass is also removed,the remaining mass is $m_2 = 400\,g = 0.4\,kg$. Let the new period be $T_2$.So,$T_2 = 2\pi \sqrt{\frac{0.4}{k}}$.Taking the ratio of the two periods:$\frac{T_2}{T_1} = \frac{2\pi \sqrt{\frac{0.4}{k}}}{2\pi \sqrt{\frac{0.9}{k}}} = \sqrt{\frac{0.4}{0.9}} = \sqrt{\frac{4}{9}} = \frac{2}{3}$.Therefore,$T_2 = T_1 	imes \frac{2}{3} = 3 	imes \frac{2}{3} = 2\,s$.

Three masses $700\,g, 500\,g$ and $400\,g$ are suspended at the end of a spring as shown and are in equilibrium. When the $700\,g$ mass is removed,the system oscillates with a period of $3\,s$. When the $500\,g$ mass is also removed,it will oscillate with a period of .... $s$.

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