When the \(700 \mathrm{~g}\) block is removed, the system has a period of oscillations of \(3 \mathrm{~s}\). If both \(700 \mathrm{~g}\) and \(500 \mathrm{~g}\) blocks are removed, the period of oscillation becomes
Three blocks of masses \(700 \mathrm{~g}, 500 \mathrm{~g}\) and \(400 \mathrm{~g}\) suspended at the end of…
When the \(700 \mathrm{~g}\) block is removed, the system has a period of oscillations of \(3 \mathrm{~s}\). If both \(700 \mathrm{~g}\) and \(500 \mathrm{~g}\) blocks are removed, the period of oscillation becomes
- \(1 \mathrm{~s}\)
- \(2 \mathrm{~s}\)
- \(3 \mathrm{~s}\)
- \(\sqrt{\frac{12}{5}} \mathrm{~s}\)
Solution
When the block of \(700 \mathrm{~g}\) is removed, then period of oscillation is given as \(\begin{aligned} T^{\prime} & =2 \pi \sqrt{\frac{m}{k}} \\ & =2 \pi \sqrt{\frac{(700+500+400-700) \times 10^{-3}}{k}} \end{aligned}\) [where, \(k=\) spring constant] \(T^{\prime}=2 \pi \sqrt{\frac{0.9}{k}}\) But \(\quad T^{\prime}=3 \mathrm{~s}\) \(\therefore \quad 3=2 \pi \sqrt{\frac{0.9}{k}} \Rightarrow 9=4 \pi^2 \times \frac{0.9}{k}\) \(\Rightarrow k=0.4 \pi^2\) ...(i) When both blocks of \(700 \mathrm{~g}\) and \(500 \mathrm{~g}\) are removed, then period of oscillation is given as \(\begin{array}{rlr} T^{\prime \prime} & =2 \pi \sqrt{\frac{(700+500+400-700-500) \times 10^{-3}}{k}} \\ & =2 \pi \sqrt{\frac{0.4}{0.4 \pi^2}} \\ & =\frac{2 \pi}{\pi}=2 \mathrm{~s} \end{array}\)
Asked in: AP EAMCET 2020 (18 Sep Shift 2)