Question

In the system shown in figure pulley is smooth. String is massless and inextensible. The acceleration of the system a, tensions $T_{1}and{T}_1(g=10{m/s}^2)$ are

• A. $\frac{20}{3}{m/s}^2,\frac{50}{3}N,\frac{60}{3}N$
• B. $\frac{10}{3}{m/s}^2,\frac{100}{3}N,\frac{60}{3}N$
• C. $\frac{20}{3}{m/s}^2,\frac{100}{3}N,\frac{60}{3}N$
• D. $\frac{20}{3}{m/s}^2,\frac{100}{3}N,\frac{50}{3}N$

Answer 1

Answer: (C)

$\frac{20}{3}{m/s}^2,\frac{100}{3}N,\frac{60}{3}N$

$\begin{array}{c}\text{From FBD of}2kg\text{block}\\ T_1-2g=2a⟶\left(1\right)\\ FBD\text{of}6kg\text{block}\\ 6g-T_2=6a⟶\left(2\right)\end{array}$

$\begin{array}{c}FBD\text{of}4kgblock\text{.}\\ T_2+4g-T_1=4a⟶\left(3\right)\end{array}$

$\begin{array}{c}\text{Adding}\left(1\right),\left(2\right),\left(3\right)\\ \begin{array}{c}{T}_1-2g+\mathrm{6g}-T_2+T_2+4g-T_1=12a\\ \Rightarrow a=\frac{8g}{12}\Rightarrow a=\frac{20}{3}m/s^2\end{array}\end{array}$

$\begin{array}{c}\text{From (1)}\\ T_1=2(g+a)=2\times \frac{50}{3}\\ T_1=\frac{100}{3}N\end{array}$

$\begin{array}{cc}\text{From}\left(2\right)& \\ \begin{array}{cc}6g& -T_2=6\left(\frac{20}{3}\right)\\ T_2& =20N\end{array}& \end{array}$