Question

Consider the situation shown in figure (5−E9). All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of acceleration of the two blocks.

Answer 1

Mass of each block is 1 kg, $\sin {\mathrm{\theta }}_1=\frac{4}{5}$, $\sin {\mathrm{\theta }}_2=\frac{3}{5}$.
The free-body diagrams for both the boxes are shown below:



mgsinθ₁ − T = ma ...(i)
T − mgsinθ₂ = ma ...(ii)

Adding equations (i) and (ii),we get:
mg(sinθ₁ − sinθ₂) = 2ma
⇒ 2a = g (sinθ₁ − sinθ₂)
$$\begin{gathered} \Rightarrow a=\frac{g}{5}\times \frac{1}{2} \\ =\frac{g}{10} \end{gathered}$$