The boxes of masses


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

  1. $0.34 \mathrm{~s}$

  2. $0.2 \mathrm{~s}$

  3. $0.25 \mathrm{~s}$

  4. $0.4 \mathrm{~s}$

Correct Option: , 4


$\left(m_{1} g-2 T\right)=m_{1} a-(1)$

$\mathrm{T}-\mathrm{m}_{2} \mathrm{~g}=\mathrm{m}_{2}(2 \mathrm{a})$

$2 \mathrm{~T}-2 \mathrm{~m}_{2} \mathrm{~g}=4 \mathrm{~m}_{2} \mathrm{a}-(2)$

$m_{1} g-2 m_{2} g=\left(m_{1}+4 m_{2}\right) a$

$a=\frac{(8-4) g}{(8+8)}=\frac{4}{16} g=\frac{g}{4}$

$a=\frac{10}{4} \mathrm{~m} / \mathrm{s}^{2}$

$\mathrm{S}=\frac{1}{2} a \mathrm{t}^{2}$

$\frac{0.2 \times 2 \times 4}{10}=\mathrm{t}^{2}$

$t=0.4 \mathrm{sec}$

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