Question

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. (use $g=10m/s^2$ )

• A. 0.34 s
• B. 0.2 s
• C. 0.25 s
• D. 0.4 s

Answer 1

Answer: (D)

$\left(m_{1}g-2T\right)=m_{1}a-(1)$
$T-m_{2}g=m_2(2a)$
$2T-2m_{2}g=4m_{2}a-(2)$
$m_{1}g-2m_{2}g=\left(m_1+4m_2\right)a$
$a=\frac{(8-4)g}{(8+8)}=\frac{4}{16}g=\frac{g}{4}$
$a=\frac{10}{4}m/s^2$
$S=\frac{1}{2}a{t}^2$
$\frac{0.2\times 2\times 4}{10}=t^2$
$t=0.4$ sec