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

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

JEE MainJEE Main 2021Laws of Motion

Solution:

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