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In the figure shown, find acceleration of the system and Tensions
$T_{1} {,T}_{2} {and T}_{3}$ $[g = 10 {m/s}^{2}]$

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$4 {m/s}^{2}, 24 N, 42 N, 14 N$

$3 {m/s}^{2}, 24 N, 43 N, 14 N$

$4 {m/s}^{2}, 24 N, 43 N, 14 N$

$4 {m/s}^{2}, 24 N, 42 N, 20 N$

answer is A.

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Detailed Solution

$a = \frac{3 + 4 - (2 + 1)}{7 + 3} \times 10 = 4 {ms}^{- 2}$

$T_{3} - 10 = 4 \Rightarrow T_{3} = 14 N$

$40 - T_{1} = 16 \Rightarrow T_{1} = 24 N$

$T_{2} + T_{1} - 30 = 12$

$T_{2} - 30 = 12$

$T_{2} = 42 N$

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