Question

Two block of masses m and 2m are connected by a light string passing over a frictionless pulley.As shown in figure, the mass m is placed on a smooth inclined plane of inclination 30${}^o$ and mass 2m hangs vertically .If the system is realesed ,the blocks move with an acceleration equal to:

• A. g / 4
• B. g / 3
• C. g / 2
• D. g

Answer 1

The correct option is C g / 2

$\begin{array}{c}a=\frac{m_2\sin \theta -m_1\sin \theta }{m_1+m_2}\\ which,inthiscaseturnsoutbe:\\ \frac{2m\times 9.8-m\times 9.8}{3m}=g\\ whichifyousolveisobviously\frac{g}{2}\end{array}$

Hence,

option $\left(C\right)$ is correct answer.