Question 99 of 210

The boxes of masses $2kg$ and $8kg$ are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass $8kg$ to strike the ground starting from rest. $\left(g=10m{s}^{-2}\right)$

A$0.25s$B$0.34s$C$0.2s$D$0.4s$

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Answer: (D) $0.4s$

\(\left(\mathrm{m}_1 \mathrm{~g}-2 \mathrm{~T}\right)=\mathrm{m}_1 \mathrm{a}-(1)\)
\(\mathrm{T}-\mathrm{m}_2 \mathrm{~g}=\mathrm{m}_2(2 \mathrm{a})\)
\(2 \mathrm{~T}-2 \mathrm{~m}_2 \mathrm{~g}=4 \mathrm{~m}_2 \mathrm{a}-(2)\)
\(\mathrm{m}_1 \mathrm{~g}-2 \mathrm{~m}_2 \mathrm{~g}=\left(\mathrm{m}_1+4 \mathrm{~m}_2\right) \mathrm{a}\)
\(\mathrm{a}=\frac{(8-4) \mathrm{g}}{(8+8)}=\frac{4}{16} \mathrm{~g}=\frac{\mathrm{g}}{4}\)
\(\mathrm{a}=\frac{10}{4} \mathrm{~m} / \mathrm{s}^2\)
\(\mathrm{~S}=\frac{1}{2} \mathrm{at}^2\)
\(\frac{0.2 \times 2 \times 4}{10}=\mathrm{t}^2\)
\(\mathrm{t}=0.4 \mathrm{sec}\)