Question
Find the acceleration of the $500\ g$ block in figure.
✓
Answer
$m_1 = 100g = 0.1kg$
$m_2 = 500g = 0.5kg$
$m_3 = 50g = 0.05kg.$
$T + 0.5a - 0.5g = 0 ...(i)$
$T_1- 0.5a - 0.05g = a ...(ii)$
$T_1 + 0.1a - T + 0.05g = 0 ...(iii)$
From equn $(ii) T_1 = 0.05g + 0.05a ...(iv)$
From equn $(i) T_1 = 0.5g - 0.5a ...(v)$
Equn $(iii)$ becomes $T_1 + 0.1a - T + 0.05g = 0$
$\Rightarrow 0.05g + 0.05a + 0.1a - 0.5g + 0.5a + 0.05g = 0$ [From (iv) and (v)]
$\Rightarrow0.65\text{a}=0.4\text{g}\Rightarrow\text{a}=\frac{0.4}{0.65}=\frac{40}{65}\text{g}=\frac{8}{13}\text{g}$ downward
Acceleration of 500gm block is $\frac{8\text{g}}{13\text{g}}$ downward
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