Question

Two blocks of masses $m_1=m$ and $m_2=2m$ are connected by a light string passing over a smooth pulley. The mass $m_1$ is placed on a smooth inclined plane of inclination $\Theta ={30}^{{}^0}$, If the system is released, the blocks move with an acceleration equal to:

• A. $\frac{g}{4}$
• B. $\frac{g}{3}$
• C. $\frac{g}{2}$
• D. $g$

Answer 1

Answer: (C)

$\frac{g}{2}$

$\begin{array}{c}theequationoftheblockare\\ T-m_{1}g\sin \theta =m_{1}a.......\left(1\right)\\ m_{2}g-T=m_{2}a..........\left(2\right)\\ Equation\left(1\right)and\left(2\right)give\\ a=\frac{\left(m_2-m_1\sin \theta \right)g}{\left(m_1+m_2\right)}\\ =\frac{\left(2m-m\times \sin {30}^o\right)g}{\left(m+2m\right)}\\ =\frac{g}{2}\\ Hence,\\ thecorrectoptionisC\end{array}$