Question

Find the acceleration of the $500g$ block given in the figure.

Answer 1

$m_1=100g=0.1kg$

$m_1=500g=0.5kg$

$m_1=50g=0.05kg$

$T+0.5a-0.5g=\mathrm{0....................}\left(i\right)$

$T_1-0.5a-0.05g=a..........\left(ii\right)$

$T_1+0.1a-T+0.05g=\mathrm{0..........}\left(iii\right)$

From equation $\left(ii\right)$

$T=0.05g+0.5a..............\left(iv\right)$

From equation $\left(i\right)$

$T_1=0.5g-0.5a..............\left(v\right)$

Equation (iii) becomes

$0.05g+0.05a+0.1a-0.5g+0.5a+0.05g=0\left[from\right(iv\left)and\right(v\left)\right]$

$0.65a=0.4g$

$a=\frac{0.4}{0.65}=\frac{40}{65}=\frac{8}{13}gdownward$