A system containing masses and pulleys connected on an inclined plane is shown in the figure. If the system is in equilibrium then the value of $m$ is

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Aicharya · Accepted Answer

According to the question, the complete situation is shown in the following figure,

Since, system is in equilibrium, hence $\begin{aligned} T & =m g \quad \ldots (i) \\ T & =(2 g-T_{1}) \sin 30^{\circ} \quad \ldots (ii) \\ T_{1} & =1 g \quad \ldots (iii) \end{aligned}$ $\therefore$ From Eqs. (ii) and (iii), we get $\begin{aligned} & T=(2 g-1 g) \sin 30^{\circ}=g \sin 30^{\circ} \\ & T=\frac{g}{2} \quad \ldots (iv) \end{aligned}$ $\therefore$ From Eqs. (i) and (iv), we get, $\begin{aligned} m g & =\frac{g}{2} \\ \Rightarrow \quad m & =0.5 \mathrm{~kg} \end{aligned}$

A system containing masses and pulleys connected on an inclined plane is shown in the figure. If the system…

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