Question

In the adjacent figures, masses of A, B and C are 1kg , 3kg and 2kg respectively then find the acceleration of the system?​

Answer 1

$\sf \large {Given - } \\ \\ \sf \: Mass \: of \: A = 1kg \\ \\ \sf \: Mass \: of \: B = 3kg \\ \\ \sf \: Mass \: of \: C = 2kg \\ \\ \sf \large {To \: Find - } \\ \\ \sf \: Accleration \: of \: the \: system \\ \\ \sf\large{Solution - }$

$\sf \: In \: the \: case \: of \: net \: pulling \: force \\ \\ \rightarrow \sf \: m_{A}g \sin60 \degree + m_{B}g \sin60 \degree - m_{C}g \sin30 \degree \\ \\ \rightarrow \sf (m_{A} + m_{B})g \sin60 \degree - m_{C}g \sin30 \degree \\ \\ \rightarrow \: (1 + 3) \times 10 \times \frac{ \sqrt{3} }{2} - 2 \times 10 \times \frac{1}{2} \\ \\ \rightarrow \: 4 \times 10 \times \frac{ \sqrt{3} }{2} - \cancel2 \times 10 \times \frac{1}{ \cancel2} \\ \\ \rightarrow \sf \: \cancel4 \times 10 \times \frac{ \sqrt{3} }{ \cancel2} - 10 \\ \\ \rightarrow \sf \: 20 \: \times \sqrt{3} - 10 \\ \\ \rightarrow \sf \: 20 \times 1.732 - 10 \\ \\ \rightarrow \sf \: 34.64 - 10 \\ \\ \rightarrow \sf \red{\large{\: 24.64N}}$

Now-

$\sf \: Total \: mass \: being \: pulled = A + B + C \\ \\ \sf \: Total \: mass \: being \: pulled = 1 + 3 + 2 \\ \\ \sf \: Total \: mass \: being \: pulled = 6 \\ \\ \large \bold{Therefore - } \\ \\ \sf \: Accleration \: of \: the \: system(a) = \frac{24.64}{6} \\ \\ \sf \: Accleration \: of \: the \: system(a) = 4.1m {s}^{ - 2} \\ \\ \large \bold{Hence - } \\ \\ \sf \: Accleration \: of \: the \: system \: is \: 4.1m {s}^{ - 2}.$

Answer 2

Explanation:

Solution is in the attachment